@article{betts_campbell_digirolamo_2021, title={EXAMINATION OF SOLVING OPTIMAL CONTROL PROBLEMS WITH DELAYS USING GPOPS-II}, volume={11}, ISSN={["2155-3297"]}, DOI={10.3934/naco.2020026}, abstractNote={There are a limited number of user-friendly, publicly available optimal control software packages that are designed to accommodate problems with delays. GPOPS-Ⅱ is a well developed MATLAB based optimal control code that was not originally designed to accommodate problems with delays. The use of GPOPS-Ⅱ on optimal control problems with delays is examined for the first time. The use of various formulations of delayed optimal control problems is also discussed. It is seen that GPOPS-Ⅱ finds a suboptimal solution when used as a direct transcription delayed optimal control problem solver but that it is often able to produce a good solution of the optimal control problem when used as a delayed boundary value solver of the necessary conditions.}, number={2}, journal={NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION}, author={Betts, John T. and Campbell, Stephen and Digirolamo, Claire}, year={2021}, month={Jun}, pages={283–305} }
 @article{betts_campbell_digirolamo_2020, title={INITIAL GUESS SENSITIVITY IN COMPUTATIONAL OPTIMAL CONTROL PROBLEMS}, volume={10}, ISSN={["2155-3297"]}, DOI={10.3934/naco.2019031}, abstractNote={An optimal control problem is presented that exhibited unexpected initial guess dependence when being solved with direct transcription methods. This note presents that example and the cautionary tale it provides.}, number={1}, journal={NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION}, author={Betts, John T. and Campbell, Stephen L. and Digirolamo, Claire}, year={2020}, month={Mar}, pages={39–43} }
 @article{campbell_kunkel_2020, title={Invariant Subspaces, Derivative Arrays, and the Computation of the Drazin Inverse}, volume={48}, ISSN={["2305-2228"]}, DOI={10.1007/s10013-020-00401-7}, abstractNote={The Drazin generalized inverse appears in a number of applications including the theory of linear time invariant differential-algebraic equations (DAEs). In this paper we consider its robust computation. Various methods are proposed all of them based on the determination of bases of invariant subspaces connected with the Drazin inverse. We also include comparisons of our methods to some of the other approaches found in the literature.}, number={4}, journal={VIETNAM JOURNAL OF MATHEMATICS}, author={Campbell, Stephen L. and Kunkel, Peter}, year={2020}, month={Dec}, pages={661–677} }
 @book{campbell_campbell_2019, title={A Problem from Genetics and the Singular Value Decomposition}, DOI={10.13140/RG.2.2.29979.92964}, author={Campbell, S.L. and Campbell, M.A.}, year={2019}, month={Jan} }
 @article{chen_cao_huang_campbell_2018, title={Decentralized Observer-Based Reliable Control for a Class of Interconnected Markov Jumped Time-Delay System Subject to Actuator Saturation and Failure}, volume={37}, ISSN={["1531-5878"]}, DOI={10.1007/s00034-018-0795-7}, number={11}, journal={CIRCUITS SYSTEMS AND SIGNAL PROCESSING}, author={Chen, Zhaohui and Cao, Zhong and Huang, Qi and Campbell, Stephen L.}, year={2018}, month={Nov}, pages={4728–4752} }
 @article{chen_cao_huang_campbell_2018, title={Reliable H-infinity control on saturated linear Markov jump system with uncertain transition rates and asynchronous jumped actuator failure}, volume={355}, ISSN={["1879-2693"]}, DOI={10.1016/j.jfranklin.2018.02.029}, abstractNote={This paper is concerned with reliable H∞ control for saturated linear Markov jump systems with uncertain transition rates and asynchronous jumped actuator failure. The actuator failures are assumed to occur randomly under the Markov process with a different jumping mode from the system jumping mode. In considering the mixed-mode-dependent state feedback controller, both H∞ stochastic stability analysis for closed-loop system with completely accessible transition rates and uncertain transition rates are investigated. Moreover, based on the obtained stability conditions, the H∞ control problems are investigated, and the controller gains can be obtained by solving a convex optimization problem with minimizing H∞ performance as objective and linear matrix inequalities (LMIs) as constraints. The problem of designing state feedback controllers such that the estimate of the domain of attraction is enlarged is also formulated and solved as an optimization problem with LMI constraints. Simulation results are presented to illustrate the effectiveness of the proposed results.}, number={9}, journal={JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS}, author={Chen, Zhaohui and Cao, Zhong and Huang, Qi and Campbell, Stephen L.}, year={2018}, month={Jun}, pages={3853–3872} }
 @article{campbell_2017, title={Comment on solution of differential-algebraic equations through gradient flow embedding}, volume={106}, ISSN={0098-1354}, url={http://dx.doi.org/10.1016/j.compchemeng.2017.07.008}, DOI={10.1016/j.compchemeng.2017.07.008}, abstractNote={The paper “On the solution of differential-algebraic equations through gradient flow embedding,” Computers and Chemical Engineering, 103 (2017), 165–173, presents an algorithm that is designed to integrate some index one DAEs. This letter reviews index one DAEs, and clarifies how the assumptions of the algorithm fit within a more general framework. The types of index one DAEs for which the new algorithm are not appropriate are discussed.}, journal={Computers & Chemical Engineering}, publisher={Elsevier BV}, author={Campbell, Stephen L.}, year={2017}, month={Nov}, pages={529–531} }
 @inbook{campbell_2016, place={Hauppauge, NY}, title={Active Fault Detection in Nonlinear Differential Algebraic Equations I: General Systems}, ISBN={978-1-53610-359-5}, booktitle={Fault Detection: Methods, Applications and Technology}, publisher={Nova Publishers}, author={Campbell, S.L.}, editor={Martin, DanielEditor}, year={2016}, pages={1–27} }
 @inbook{campbell_scott_2016, place={Hauppauge, NY}, title={Active Fault Detection in Nonlinear Differential Algebraic Equations II: Using Linearizations}, booktitle={Fault Detection: Methods, Applications and Technology}, publisher={Nova Publishers}, author={Campbell, S.L. and Scott, J.R.}, editor={Martin, DanielEditor}, year={2016}, pages={29–51} }
 @inproceedings{campbell_owen_2016, title={Actuator effects on auxiliary signal design for failure detection}, ISBN={9781509022465}, url={http://dx.doi.org/10.1109/SECON.2016.7506748}, DOI={10.1109/secon.2016.7506748}, abstractNote={Fault detection and identification (FDI) are important tasks in most modern industrial systems and processes. A variety of approaches both active and passive have been investigated. In much of the active work the focus was on designing an optimal test signal. However, much less attention was given to actually generating that test signal. Here the effect of including actuator effects in generating an optimal test signal for active fault detection is investigated.}, booktitle={SoutheastCon 2016}, publisher={IEEE}, author={Campbell, Stephen L. and Owen, Hailey}, year={2016}, month={Mar} }
 @inproceedings{campbell_scott_2016, title={Auxiliary signal design for failure detection with initial prior information}, ISBN={9781509022465}, url={http://dx.doi.org/10.1109/SECON.2016.7506738}, DOI={10.1109/secon.2016.7506738}, abstractNote={Fault detection and the related problem of identification (FDI) play an important role in many modern technological systems and processes. A variety of active and passive approaches have been investigated. Previous work on auxiliary signal design for one active approach used a bound on total uncertainty which included the state at the start of the test as part of a cost function. However, in some applications that may not be the most natural thing to do if there is some information about prior behavior. Using this prior information in a different way leads to several changes in algorithms and software. This paper investigates these changes and their consequences.}, booktitle={SoutheastCon 2016}, publisher={IEEE}, author={Campbell, Stephen L. and Scott, Jason R.}, year={2016}, month={Mar} }
 @article{campbell_betts_2016, title={Comments on direct transcription solution of DAE constrained optimal control problems with two discretization approaches}, volume={73}, ISSN={["1572-9265"]}, DOI={10.1007/s11075-016-0119-6}, number={3}, journal={NUMERICAL ALGORITHMS}, author={Campbell, Stephen L. and Betts, John T.}, year={2016}, month={Nov}, pages={807–838} }
 @article{campbell_kunkel_2016, title={Solving higher index DAE optimal control problems}, volume={6}, ISSN={2155-3289}, url={http://dx.doi.org/10.3934/naco.2016020}, DOI={10.3934/naco.2016020}, abstractNote={A number of methods have been proposed for solving optimal control problems where the process being optimized 
is described by a differential algebraic equation (DAE). However, many of these methods require special circumstances 
to hold or the user to have special software. In this paper we go over many of these options and discuss 
what is usually necessary for them to be successful. We use a nonlinear index three control problem 
to illustrate many of our observations..}, number={4}, journal={Numerical Algebra, Control and Optimization}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Campbell, Stephen and Kunkel, Peter}, year={2016}, month={Dec}, pages={447–472} }
 @article{betts_campbell_thompson_2016, title={Solving optimal control problems with control delays using direct transcription}, volume={108}, ISSN={["1873-5460"]}, DOI={10.1016/j.apnum.2015.12.008}, abstractNote={The numerical treatment of optimal control problems with state and control delays is important in a wide variety of scientific and technical applications. Solutions to these types of problems are difficult to obtain via analytic techniques since the system may be nonlinear and subjected to complicated inputs and constraints. There are several numerical methods available to compute the solutions of optimal control problems without delays. One such popular method is direct transcription. Although the numerical solutions of optimal control delay problems are important, less literature and software exists in this area. A general purpose industrial grade direct transcription code that can handle optimal control problems with both state and control constraints and delays is under development. Control delays pose a special challenge. A new technique for treating control delays when using a direct transcription approach is investigated in this paper.}, journal={APPLIED NUMERICAL MATHEMATICS}, author={Betts, John T. and Campbell, Stephen L. and Thompson, Karmethia C.}, year={2016}, month={Oct}, pages={185–203} }
 @inproceedings{zhang_campbell_2015, title={Robust finite-time filtering for singular discrete-time stochastic systems}, DOI={10.1109/ccdc.2015.7162049}, abstractNote={This paper addresses the problem of singular stochastic finite-time filter design for uncertain discrete-time singular stochastic systems. The stochastic Lyapunov function method is adopted to design a filter such that for all admissible uncertainties, the filtering error system is singular stochastic finite-time stable (SSFTS) and preserves a prescribed performance level. A sufficient condition for the existence of a filter for the system under consideration is developed and the corresponding filter parameters can be calculated by solving a sequence of linear matrix inequalities (LMI). Finally, a numerical example is given to illustrate the design procedure and the effectiveness of the proposed method.}, booktitle={2015 27th chinese control and decision conference (ccdc)}, author={Zhang, A. Q. and Campbell, Stephen}, year={2015}, pages={913–918} }
 @inbook{campbell_2015, title={The Flexibility of DAE Formulations}, ISBN={9783319224275 9783319224282}, ISSN={2199-7497 2199-840X}, url={http://dx.doi.org/10.1007/978-3-319-22428-2_1}, DOI={10.1007/978-3-319-22428-2_1}, abstractNote={There has been extensive research on DAEs and their applications. One major reason given for the usefulness of DAEs is that they are the initial way that many complex systems are most naturally modeled. But there are other ways that DAE formulations are useful. This survey focuses on a number of problems where the extra flexibility of a DAE formulation permits the solution of a problem that would be hard to solve otherwise.}, booktitle={Surveys in Differential-Algebraic Equations III}, publisher={Springer International Publishing}, author={Campbell, Stephen L.}, year={2015}, pages={1–59} }
 @inproceedings{campbell_scott_2014, title={Asynchronous auxiliary signal design for failure detection}, ISBN={9781479938407}, url={http://dx.doi.org/10.1109/smc.2014.6974340}, DOI={10.1109/smc.2014.6974340}, abstractNote={Fault detection and identification (FDI) are important tasks in most modern industrial systems and processes. A variety of approaches both active and passive have been investigated. A test signal or input is used in an active approach. Usually in the active approach the same time window is used for the running of the test and the application of the test signal. However, that is not always the most desirable or practical thing to do. The effect of different signal and observation windows is investigated here for one active approach.}, booktitle={2014 IEEE International Conference on Systems, Man, and Cybernetics (SMC)}, publisher={IEEE}, author={Campbell, Stephen L. and Scott, Jason R.}, year={2014}, month={Oct} }
 @article{campbell_scott_2014, title={Auxiliary signal design for failure detection in differential-algebraic equations}, volume={4}, ISSN={2155-3289}, url={http://dx.doi.org/10.3934/naco.2014.4.151}, DOI={10.3934/naco.2014.4.151}, abstractNote={Fault detection and identification (FDI) are important tasks in most modern industrial and mechanical systems and processes. Many of these systems are most naturally modeled by differential-algebraic equations (DAE). This paper addresses active fault detection in DAE. A technique is presented to calculate an auxiliary test signal guaranteeing detection, assuming bounded additive noise. An efficient real time detection algorithm is also provided as are example simulations. The extension to model uncertainty is discussed.}, number={2}, journal={Numerical Algebra, Control and Optimization}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Campbell, Stephen and Scott, Jason}, year={2014}, month={May}, pages={151–179} }
 @inproceedings{scott_campbell_2014, title={Auxiliary signal design for failure detection in high index differential-algebraic equations}, ISBN={9781467360906 9781479977468 9781479977451}, url={http://dx.doi.org/10.1109/cdc.2014.7040395}, DOI={10.1109/cdc.2014.7040395}, abstractNote={Auxiliary test signals for active fault detection have been studied by several authors but traditionally for systems with discrete time or continuous time nonimpulsive causal models. Recently, a method for designing test signals for systems modeled by higher index differential algebraic equations has been developed. This paper examines more carefully when such a test signal exists and also how to get a useful test signal when the previous algorithm breaks down.}, booktitle={53rd IEEE Conference on Decision and Control}, publisher={IEEE}, author={Scott, Jason R. and Campbell, Stephen L.}, year={2014}, month={Dec} }
 @inbook{bobinyec_campbell_2014, title={Linear Differential Algebraic Equations and Observers}, ISBN={9783319110493 9783319110509}, ISSN={2199-7497 2199-840X}, url={http://dx.doi.org/10.1007/978-3-319-11050-9_1}, DOI={10.1007/978-3-319-11050-9_1}, abstractNote={Observers play an important role in the control of linear systems. Given the importance of DAE models, it is natural that there has been considerable interest in designing and using observers for DAEs. The first part of this paper surveys some aspects of DAEs and observers that lay the foundation for the second part which discusses a recent general approach to observer design for linear DAEs using completions. This approach also holds great promise for nonlinear DAEs.}, booktitle={Surveys in Differential-Algebraic Equations II}, publisher={Springer International Publishing}, author={Bobinyec, Karen S. and Campbell, Stephen L.}, year={2014}, month={Nov}, pages={1–67} }
 @article{betts_campbell_thompson_2015, title={Lobatto IIIA methods, direct transcription, and DAEs with delays}, volume={69}, ISSN={["1572-9265"]}, DOI={10.1007/s11075-014-9896-y}, number={2}, journal={NUMERICAL ALGORITHMS}, author={Betts, John T. and Campbell, Stephen L. and Thompson, Karmethia}, year={2015}, month={Jun}, pages={291–300} }
 @inproceedings{betts_campbell_thompson_2013, title={Direct Transcription Solution of Optimal Control Problems with Differential Algebraic Equations with Delays}, ISBN={9780889869615}, url={http://dx.doi.org/10.2316/p.2013.807-003}, DOI={10.2316/p.2013.807-003}, abstractNote={Many physical systems are naturally modeled as differential algebraic equations or DAEs. Many physical systems also possess delays either in the dynamics or in the application of the control. Direct transcription is a popular approach in industry for numerically solving nondelayed optimal control problems because of its ability to handle problems with constraints. This paper reports on progress in developing an industrial strength direct transcription optimal control software package that can solve many problems with delays and DAE models. In particular, we focus in this paper on how the use of the DAE formalism allows for the consideration of a much greater variety of delays.}, booktitle={Power and Energy / 807: Intelligent Systems and Control / 808: Technology for Education and Learning}, publisher={ACTAPRESS}, author={Betts, John T. and Campbell, Stephen L. and Thompson, Karmethia C.}, year={2013} }
 @article{campbell_holte_2013, title={Eigenvalue placement in completions of DAES}, volume={26}, DOI={10.13001/1081-3810.1667}, abstractNote={Differential algebraic equations (DAEs) are used to describe many physical processes. A completion of a DAE is an ordinary differential equation whose solutions include those of the DAE. Algorithms exists for designing stabilized completions of differential algebraic equations. Recent work on observers for DAEs has shown the need for more information on, and control of the placement of, the additional eigenvalues of the completion. This paper investigates this eigenvalue placement problem. Results are given relating the additional eigenvalues of the completion and the choice of stabilization matrix for certain important classes of linear DAEs.}, number={1}, journal={Electronic Journal of Linear Algebra}, publisher={University of Wyoming Libraries}, author={Campbell, Stephen L. and Holte, Lise E.}, year={2013}, month={Jan}, pages={520–534} }
 @inbook{scott_campbell_2013, title={Observer based fault detection in differential algebraic equations}, ISBN={9781611973273}, url={http://dx.doi.org/10.1137/1.9781611973273.24}, DOI={10.1137/1.9781611973273.24}, abstractNote={Fault detection is an important part of most modern industrial systems and processes. One approach to fault detection is based on the use of observers. Many physical processes are most naturally modeled by differential algebraic equations. Recently there has been significant progress in the design of observers for complex differential algebraic equations. This paper examines the use of observers for fault detection in systems modeled by differential algebraic equations.}, booktitle={2013 Proceedings of the Conference on Control and its Applications}, publisher={Society for Industrial and Applied Mathematics}, author={Scott, Jason R. and Campbell, Stephen L.}, year={2013}, month={Jul}, pages={176–183} }
 @article{campbell_kunkel_2013, title={On the numerical treatment of linear-quadratic optimal control problems for general linear time-varying differential-algebraic equations}, volume={242}, ISSN={["1879-1778"]}, DOI={10.1016/j.cam.2012.10.011}, abstractNote={The development of numerical methods for finding optimal solutions of control problems modeled by differential-algebraic equations (DAEs) is an important task. Usually restrictions are placed on the DAE such as being semi-explicit. Here the numerical solution of optimal control problems with linear time-varying DAEs as the process and quadratic cost functionals is considered. The leading coefficient is allowed to be time-varying and the DAE may be of higher index. Both a direct transcription approach and the solution of the necessary conditions are examined for two important discretizations.}, journal={JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS}, author={Campbell, Stephen L. and Kunkel, Peter}, year={2013}, month={Apr}, pages={213–231} }
 @inproceedings{betts_campbell_thompson_2013, place={San Diego}, title={Simulation and Optimization of Systems with Delays}, booktitle={Proceedings of the 2013 Spring Simulation Multiconference Poster Session}, publisher={Society for Computer Simulation International}, author={Betts, J.T. and Campbell, S.L. and Thompson, K.}, year={2013}, pages={1084–1085} }
 @article{campbell_kunkel_bobinyec_2012, title={A minimal norm corrected underdetermined Gauss-Newton procedure}, volume={62}, DOI={10.1016/j.apnum.2012.01.006}, abstractNote={If a Gauß–Newton iteration is used to solve a system of equations that has a manifold of solutions, then the iteration does not produce the minimal norm solution. The limit of the iteration depends on the starting point. This paper introduces a modified Gauß–Newton method that is designed to keep the nonunique part of the solution small in some sense. The iteration is analyzed. Its behavior is discussed along with two computational examples that include the iteration's application to general integration methods for differential algebraic equations.}, number={5}, journal={Applied Numerical Mathematics}, author={Campbell, Stephen and Kunkel, P. and Bobinyec, K.}, year={2012}, pages={592–605} }
 @article{ashari_nikoukhah_campbell_2012, title={Active Robust Fault Detection in Closed-Loop Systems: Quadratic Optimization Approach}, volume={57}, ISSN={["1558-2523"]}, DOI={10.1109/tac.2012.2188430}, abstractNote={Active fault detection consists of finding an auxiliary input signal such that its use allows detection of faults using a multi-model framework. Faults can be detected during a test period that would otherwise not be possible to detect during normal operation using passive tests. In this paper, we consider the problem of optimal exogenous signal design for a linear uncertain system controlled by a linear feedback. This signal design is based on controller design criteria of linear quadratic regulators (LQR). Optimal exogenous signal design for short test periods is considered first. An efficient method is developed to solve the corresponding finite time-horizon optimization problem. Then the asymptotic behavior of the robust fault detection problem and its stationary optimal solution is considered. The optimal exogenous signal for the stationary case is given based on a frequency analysis of the solution. This signal can be used as an approximation on longer interval finite time-horizons. It is shown that a suitable feedback can reduce the cost function compared with the open-loop case.}, number={10}, journal={IEEE Transactions on Automatic Control}, author={Ashari, A.E. and Nikoukhah, R. and Campbell, S.L.}, year={2012}, month={Oct}, pages={592–605} }
 @inbook{betts_campbell_thompson_2012, title={Chapter 10: Optimal Control of a Delay PDE}, ISBN={9781611972245 9781611972252}, url={http://dx.doi.org/10.1137/9781611972252.ch10}, DOI={10.1137/9781611972252.ch10}, booktitle={Control and Optimization with Differential-Algebraic Constraints}, publisher={Society for Industrial and Applied Mathematics}, author={Betts, John T. and Campbell, Stephen L. and Thompson, Karmethia C.}, year={2012}, month={Jan}, pages={213–231} }
 @inproceedings{bobinyec_campbell_kunkel_2012, title={Constructing observers for linear time varying DAEs}, DOI={10.1109/cdc.2012.6426989}, abstractNote={This paper presents an approach for the construction of both full order and reduced order observers for general linear time varying differential algebraic equations. The necessary theory is presented. Computational issues are elaborated on, and a six dimensional example of an index two electrical circuit is solved as an illustration.}, booktitle={2012 IEEE 51st IEEE Conference on Decision and Control (CDC)}, publisher={IEEE}, author={Bobinyec, Karen and Campbell, Stephen L. and Kunkel, Peter}, year={2012}, pages={5749–5754} }
 @book{biegler_campbell_mehrmann_2012, title={Control and Optimization with Differential-Algebraic Constraints}, DOI={10.1137/9781611972252}, abstractNote={Differential-algebraic equations are the most natural way to mathematically model many complex systems in science and engineering. Once the model is derived, it is important to optimize the design parameters and control it in the most robust and efficient way to maximize performance. This book presents the latest theory and numerical methods for the optimal control of differential-algebraic equations. Readers will find the following features presented in a readable fashion so the results are accessible to the widest audience: the most recent theory, written by leading experts from a number of academic and nonacademic areas and departments, several state-of-the-art numerical methods, and real-world applications. Audience: This book is intended for applied mathematicians, engineers, and computational scientists from a variety of disciplines who are interested in the optimal control of problems. It will be of interest to those developing methods and theory and those working on real-world applications, especially in control and chemical and mechanical engineering. Contents: Chapter 1: DAEs, Control, and Optimization; Chapter 2: Regularization of Linear and Nonlinear Descriptor Systems; Chapter 3: Notes on Linearization of DAEs and on Optimization with Differential-Algebraic Constraints; Chapter 4: Spectra and Leading Directions for Linear DAEs; Chapter 5: StratiGraph Tool: Matrix Stratifications in Control Applications; Chapter 6: Descriptor System Techniques in Solving H2/Infinity-Optimal Fault Detection and Isolation Problems; Chapter 7: Normal Forms, High-Gain, and Funnel Control for Linear Differential-Algebraic Systems; Chapter 8: Linear-Quadratic Optimal Control Problems with Switch Points and a Small Parameter; Chapter 9: Mixed-Integer DAE Optimal Control Problems: Necessary Conditions and Bounds; Chapter 10: Optimal Control of a Delay PDE; Chapter 11: Direct Transcription with Moving Finite Elements; Chapter 12: Solving Parameter Estimation Problems with SOCX; Chapter 13: Control of Integrated Chemical Process Systems Using Underlying DAE Models; Chapter 14: DMPC for Building Temperature Regulation; Chapter 15: Dynamic Regularization, Level Set Shape Optimization, and Computed Myography; Chapter 16: The Application of Pontryagin s Minimum Principle for Endpoint Optimization of Batch Processes}, publisher={Society for Industrial and Applied Mathematics}, year={2012}, month={Jan} }
 @book{biegler_campbell_mehrmann_2012, place={Philadelphia, PA}, series={Advances in Design and Control}, title={Control and Optimization with Differential-Algebraic Constraints}, ISBN={9781611972245}, publisher={Society for Industrial and Applied Mathematics}, year={2012}, collection={Advances in Design and Control} }
 @article{ashari_nikoukhah_campbell_2012, title={Effects of feedback on active fault detection}, volume={48}, ISSN={["1873-2836"]}, DOI={10.1016/j.automatica.2012.02.020}, abstractNote={In recent years there has been increased interest in the use of active approaches for fault detection. In one of these approaches an auxiliary signal is designed such that over a short period it will reveal a fault not otherwise detectable and do so with as little perturbation of system performance as possible. This method is robust in the sense of guaranteeing the detection of the fault for a whole set of bounded uncertainties. Feedback plays an important role in control but its role in active fault detection based on auxiliary signals has not been explored, yet. This paper begins that investigation.}, number={5}, journal={AUTOMATICA}, author={Ashari, Alireza Esna and Nikoukhah, Ramine and Campbell, Stephen L.}, year={2012}, month={May}, pages={866–872} }
 @inproceedings{campbell_kunkel_mehrmann_2012, title={Regularization of linear and nonlinear descriptor systems}, DOI={10.1137/9781611972252.ch2}, number={23}, booktitle={Control and optimization with differential-algebraic constraints}, author={Campbell, Stephen and Kunkel, P. and Mehrmann, V.}, year={2012}, pages={17–36} }
 @article{stephen_martene_2011, title={Active incipient fault detection in continuous time systems with multiple simultaneous faults}, volume={1}, ISSN={2155-3289}, url={http://dx.doi.org/10.3934/naco.2011.1.211}, DOI={10.3934/naco.2011.1.211}, abstractNote={The problem of detecting small parameter variations 
in linear uncertain systems due to incipient faults, with the possibility of injecting 
an input signal to enhance detection, is considered. Most studies assume that there is only one fault developing. Recently an active approach for two or more simultaneous faults has been introduced for the discrete time case. In this paper we extend this approach to the continuous time case. A computational method 
for the construction of an input signal for achieving 
guaranteed detection with specified precision is presented. 
The method is an extension of a multi-model approach used 
for the construction of auxiliary signals for failure detection, however, new technical issues must be addressed.}, number={2}, journal={Numerical Algebra, Control and Optimization}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Stephen, Campbell and Martene, Fair}, year={2011}, month={Jun}, pages={211–224} }
 @article{ashari_nikoukhah_campbell_2011, title={Auxiliary signal design for robust active fault detection of linear discrete-time systems}, volume={47}, ISSN={["1873-2836"]}, DOI={10.1016/j.automatica.2011.06.009}, abstractNote={In this paper, algorithms are proposed to design auxiliary signals for active fault detection based on a multi-model formulation of discrete-time systems. Two different scenarios are considered for this problem; the first one assumes there is no a priori information on initial conditions and no exogenous input signal, while the second allows for having a priori information and the possibility of having a known input in addition to the test signal. Approaches are proposed for solving these two types of problems which are capable of solving the problems efficiently. This is achieved by using a recursive approach based on the use of special Riccati equations. These algorithms can be used for systems of higher dimension and on longer time horizons than the existing methods.}, number={9}, journal={AUTOMATICA}, author={Ashari, Alireza Esna and Nikoukhah, Ramine and Campbell, Stephen L.}, year={2011}, month={Sep}, pages={1887–1895} }
 @inproceedings{betts_campbell_thompson_simos_psihoyios_tsitouras_anastassi_2011, title={Direct Transcription Solution of Optimal Control Problems with Control Delays}, url={http://dx.doi.org/10.1063/1.3636665}, DOI={10.1063/1.3636665}, abstractNote={The numerical solution of optimal control problems is important in many areas. Often the models for these problems have delays. Direct transcription is a popular approach for the numerical solution of optimal control problems in industry. However, much less work has been done on the direct transcription solution of optimal control problems with delays. This talk will describe progress and challenges in developing a general purpose industrial grade direct transcription code that can handle problems with delays. Of special interest will be the more challenging case of control delays.}, publisher={AIP}, author={Betts, John T. and Campbell, Stephen L. and Thompson, Karmethia C. and Simos, Theodore E. and Psihoyios, George and Tsitouras, Ch. and Anastassi, Zacharias}, year={2011} }
 @inproceedings{andjelkovic_campbell_2011, title={Direct optimization determination of auxiliary test signals for linear problems with model uncertainty}, ISBN={9781612848013 9781612848006 9781467304573 9781612847993}, url={http://dx.doi.org/10.1109/cdc.2011.6160186}, DOI={10.1109/cdc.2011.6160186}, abstractNote={Recently there has been increased interest in active approaches for fault detection which use auxiliary test signals. Theory and algorithms have been presented in the literature for the design of fault detection signals for linear systems with model uncertainty. These approaches cannot solve many problems with constraints. This paper gives the first direct optimization formulation of the more general constrained problem. The use of a direct optimization formulation allows the solution of problems not possible by the original algorithms such as problems with input and state constraints. Computational examples are given both to illustrate the theory and to discuss computational issues.}, booktitle={IEEE Conference on Decision and Control and European Control Conference}, publisher={IEEE}, author={Andjelkovic, Ivan and Campbell, Stephen L.}, year={2011}, month={Dec} }
 @inproceedings{betts_campbell_thompson_2011, title={Direct transcription solution of optimal control problems with delays}, volume={1389}, booktitle={Numerical Analysis and Applied Mathematics ICNAAM2011 AIP Conf. Proc.}, author={Betts, J.T. and Campbell, S.L. and Thompson, Karmethia}, year={2011}, pages={38–41} }
 @inproceedings{bobinyec_campbell_kunkel_2011, title={Full order observers for linear DAEs}, ISBN={9781612848013 9781612848006 9781467304573 9781612847993}, url={http://dx.doi.org/10.1109/cdc.2011.6160215}, DOI={10.1109/cdc.2011.6160215}, abstractNote={Observer design for descriptor systems, or systems of differential algebraic equations (DAEs) as they are also known, is well studied in the linear time invariant (LTI) case. However, those studies do not readily extend to general linear time varying (LTV) or nonlinear descriptor systems. This paper presents an alternative approach for observer design that not only works for the LTI case but also shows great potential for the design of observers for general LTV descriptor systems.}, booktitle={IEEE Conference on Decision and Control and European Control Conference}, publisher={IEEE}, author={Bobinyec, Karen and Campbell, Stephen L. and Kunkel, Peter}, year={2011}, month={Dec} }
 @inproceedings{bobinyec_campbell_kunkel_2011, title={Maximally reduced observers for linear time varying DAEs}, ISBN={9781457710667}, url={http://dx.doi.org/10.1109/cacsd.2011.6044570}, DOI={10.1109/cacsd.2011.6044570}, abstractNote={The problem of observer design for descriptor systems, or systems of differential algebraic equations (DAEs) as they are also known, has been studied in the linear time invariant case. However, those studies do not readily extend to general linear time varying descriptor systems. Recently there have been new theoretical results and algorithms for computing completions of DAEs. In this paper we examine the application of these ideas to the computation of reduced order observers for linear time invariant and linear time varying DAEs.}, booktitle={2011 IEEE International Symposium on Computer-Aided Control System Design (CACSD)}, publisher={IEEE}, author={Bobinyec, Karen and Campbell, Stephen L. and Kunkel, Peter}, year={2011}, month={Sep} }
 @inproceedings{betts_campbell_thompson_2011, title={Optimal control software for constrained nonlinear systems with delays}, ISBN={9781457710667}, url={http://dx.doi.org/10.1109/cacsd.2011.6044560}, DOI={10.1109/cacsd.2011.6044560}, abstractNote={The numerical solution of optimal control problems is important in a variety of industries. One of the popular methods for complex problems is direct transcription. Direct transcription does not rely on the necessary conditions and it is easy to incorporate a wide variety of constraints on both controls and states. Optimal control problems can often involve delays in the state or the control or both. While some numerical methods exist for some optimal control problems with delays they are not direct transcription methods. This paper reports on progress in developing a general purpose industrial grade software package to numerically solve complex optimal control problems with delays and state and control constraints using direct transcription.}, booktitle={2011 IEEE International Symposium on Computer-Aided Control System Design (CACSD)}, publisher={IEEE}, author={Betts, John T. and Campbell, Stephen L. and Thompson, Karmethia C.}, year={2011}, month={Sep} }
 @article{nikoukhah_campbell_drake_2010, title={An active approach for detection of incipient faults}, volume={41}, ISSN={["1464-5319"]}, DOI={10.1080/00207720903045817}, abstractNote={The methodology of auxiliary signal design for robust fault detection based on a multi-model (MM) formulation of normal and faulty systems is used to study the problem of incipient fault detection. The fault is modelled as a drift in a system parameter, and an auxiliary signal is to be designed to enhance the detection of variations in this parameter. It is shown that it is possible to consider the model of the system with a drifted parameter as a second model and use the MM framework for designing the auxiliary signal by considering the limiting case as the parameter variation goes to zero. The result can be applied very effectively to many early detection problems where small parameter variations should be detected. Two different approaches for computing the test signal are given and compared on several computational examples.}, number={2}, journal={INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE}, author={Nikoukhah, R. and Campbell, S. L. and Drake, K.}, year={2010}, pages={241–257} }
 @book{campbell_chancelier_nikoukhah_2010, title={Modeling and Simulation in Scilab/Scicos with ScicosLab 4.4}, DOI={10.1007/978-1-4419-5527-2}, abstractNote={Scilab is a free open-source software package for scientific computation. It includes hundreds of general purpose and specialized functions for numerical computation, organized in libraries called too}, publisher={Springer New York}, author={Campbell, Stephen L. and Chancelier, Jean-Philippe and Nikoukhah, Ramine}, year={2010} }
 @inproceedings{bobinyec_campbell_kunkel_2010, place={Atlanta}, title={Stabilized Completions of Differential Algebraic Equations and the Design of Observers}, booktitle={Proceedings of Neural, Parallel, and Scientific Computation}, author={Bobinyec, K. and Campbell, S.L. and Kunkel, P.}, year={2010} }
 @article{campbell_nikoukhah_2010, title={Teaching Introductory Differential Equations with ScicosLab}, volume={7}, ISSN={2160-5211}, url={http://dx.doi.org/10.5642/codee.201007.01.02}, DOI={10.5642/codee.201007.01.02}, abstractNote={Perhaps the largest and most capable open source software for doing applied mathematics is the open source package Scicoslab. Widely used in Europe and Asia it is less well known in the United States. In this article we will explain how ScicosLab can be easily used to help teach differential equations and to also introduce students to a software package that they can take with them for the rest of their careers.}, number={1}, journal={CODEE Journal}, publisher={Claremont Colleges Library}, author={Campbell, Stephen and Nikoukhah, Ramine}, year={2010}, pages={1–12} }
 @article{sweetingham_campbella_2009, title={AUXILIARY SIGNAL DESIGN FOR FAULT DETECTION IN NONLINEAR SYSTEMS}, volume={37}, ISSN={1925-5810}, url={http://dx.doi.org/10.2316/journal.201.2009.3.201-2049}, DOI={10.2316/journal.201.2009.3.201-2049}, abstractNote={Recently, there has been considerable research on active fault detection and model identification algorithms for linear systems. These algorithms compute an auxiliary input signal which guarantees fault detection, assuming a bounded noise. This paper begins to address the issue of applying the previously developed linear theory to nonlinear systems. To exploit the known linear theory, linearizations are used and bounds are computed to find the allowable noise for the nonlinear system. We also present an example of an oscillating pendulum to verify the bounds computed.}, number={3}, journal={Control and Intelligent Systems}, publisher={ACTA Press}, author={Sweetingham, K.A. and Campbella, S.L.}, year={2009} }
 @article{fair_campbell_2009, title={Active incipient fault detection with more than two simultaneous faults}, ISBN={["978-1-4244-2793-2"]}, ISSN={["1062-922X"]}, DOI={10.1109/icsmc.2009.5346202}, abstractNote={The problem of detecting small parameter variations in linear uncertain systems due to incipient faults, with the possibility of injecting an input signal to enhance detection, is considered. Most studies assume that there is only one fault developing. Recently an active approach for two simultaneous faults has been introduced. In this paper we extend this approach to allow for more than two simultaneous faults. Having more than two simultaneous incipient faults is sometimes a natural assumption. A computational method for the construction of an input signal for achieving guaranteed detection with specified precision is presented for discrete time systems. The method is an extension of a multi-model approach used for the construction of auxiliary signals for failure detection, however, new technical issues must be addressed. A case study is examined.}, journal={2009 IEEE INTERNATIONAL CONFERENCE ON SYSTEMS, MAN AND CYBERNETICS (SMC 2009), VOLS 1-9}, publisher={IEEE}, author={Fair, Martene and Campbell, Stephen L.}, year={2009}, pages={3322–3327} }
 @article{fair_campbell_2009, title={Active incipient fault detection with two simultaneous faults}, volume={42}, ISSN={1474-6670}, url={http://dx.doi.org/10.3182/20090630-4-es-2003.00095}, DOI={10.3182/20090630-4-es-2003.00095}, abstractNote={Abstract The problem of detecting small parameter variations in linear uncertain systems due to incipient faults, by injecting an input signal to enhance detection is considered. Unlike previous work where it is usually assumed that there is only one fault, in this paper we allow for two faults which is a natural assumption in the incipient case. A constructive method for the construction of an optimal input signal for achieving guaranteed detection with specified precision is presented in the discrete model case. The method is an extension of the multi-model approach used for the construction of auxiliary signals for failure detection, however, new technical issues must be addressed.}, number={8}, journal={IFAC Proceedings Volumes}, publisher={Elsevier BV}, author={Fair, Martene and Campbell, Stephen L.}, year={2009}, pages={573–578} }
 @article{ashari_nikoukhah_campbell_2009, title={Active robust fault detection of closed-loop systems: general cost case}, volume={42}, url={https://doi.org/10.3182/20090630-4-ES-2003.00097}, DOI={10.3182/20090630-4-ES-2003.00097}, abstractNote={Abstract Active failure detection consists of finding an input signal (auxiliary signal) such that its use allows perfect detection of faults in a multi-model framework. In this paper we consider the problem of optimal auxiliary signal design for a linear uncertain system controlled by a linear feedback. The optimization criterion used is a worst case quadratic cost, which in practice is the same cost used for the design of the controller. Even though we suppose that the feedback controller is given, the methodology developed here should be useful for feedback design to achieve both control and fault detection objectives.}, number={8}, journal={IFAC Proceedings Volumes}, author={Ashari, A.E. and Nikoukhah, R. and Campbell, S.L.}, year={2009}, pages={585–590} }
 @article{okay_campbell_kunkel_2009, title={Completions of implicitly defined linear time varying vector fields}, volume={431}, ISSN={["1873-1856"]}, DOI={10.1016/j.laa.2009.05.006}, abstractNote={The stabilization of constraints through such techniques as Baumgarte stabilization has been used in the simulation community for some time. This and a number of control problems can be viewed as either extending, or modifying, a vector field off of some manifold. Generally these approaches required the equations to have a special structure. Motivated by numerical simulation there has recently been new progress on doing this stabilization in numerically robust ways for larger classes of systems. In this paper we point out how earlier linear time invariant results do not immediately apply to the linear time varying case and then analyze the linear time varying case.}, number={9}, journal={LINEAR ALGEBRA AND ITS APPLICATIONS}, author={Okay, Irfan and Campbell, Stephen L. and Kunkel, Peter}, year={2009}, month={Oct}, pages={1422–1438} }
 @article{campbell_kunkel_2009, title={Completions of nonlinear DAE flows based on index reduction techniques and their stabilization}, volume={233}, ISSN={["1879-1778"]}, DOI={10.1016/j.cam.2009.08.111}, abstractNote={Differential algebraic equations (DAEs) define a differential equation on a manifold. A number of ways have been developed to numerically solve some classes of DAEs. Motivated by problems in control theory, numerical simulation, and the use of general purpose modeling environments, recent research has considered the embedding of the DAE solutions of a general DAE into the solutions of an ODE where the added dynamics have special properties. This paper both provides new results on the linear time-varying case and considers the important nonlinear case.}, number={4}, journal={JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS}, author={Campbell, Stephen L. and Kunkel, Peter}, year={2009}, month={Dec}, pages={1021–1034} }
 @article{ashari_nikoukhah_campbell_2009, title={Feedback in Active Fault Detection}, volume={42}, ISSN={1474-6670}, url={http://dx.doi.org/10.3182/20090706-3-fr-2004.00032}, DOI={10.3182/20090706-3-fr-2004.00032}, abstractNote={Abstract In recent years there has been increased interest in the use of active approaches toward fault detection. In one of these approaches a test signal is designed such that over a short period it will reveal a fault not otherwise detectable and do so with as little perturbation of system performance as possible. Feedback plays an important role in control but its role in active fault detection based on test signals has not been explored. This paper begins that investigation.}, number={10}, journal={IFAC Proceedings Volumes}, publisher={Elsevier BV}, author={Ashari, Alireza Esna and Nikoukhah, Ramine and Campbell, Stephen L.}, year={2009}, pages={192–196} }
 @book{campbell_meyer_2009, title={Generalized Inverses of Linear Transformations}, volume={56}, ISBN={["978-0-898716-71-9"]}, DOI={10.1137/1.9780898719048}, abstractNote={Preface to the Classics edition Preface Introduction and other preliminaries 1. The Moore-Penrose or generalized inverse 2. Least squares solutions 3. Sums, partitioned matrices and the constrained generalized inverse 4. Partial isometries and EP matrices 5. The generalized inverse in electrical engineering 6. (i, j, k)-Generalized inverses and linear estimation 7. The Drazin inverse 8. Applications of the Drazin inverse to the theory of finite Markov chains 9. Applications of the Drazin inverse 10. Continuity of the generalized inverse 11. Linear programming 12. Computational concerns Bibliography Index.}, journal={GENERALIZED INVERSES OF LINEAR TRANSFORMATIONS}, publisher={Society for Industrial and Applied Mathematics}, author={Campbell, Stephen L. and Meyer, Carl D.}, year={2009}, pages={1–272} }
 @inproceedings{valdez-jasso_haider_campbell_bia_zocalo_armentano_olufsen_2009, title={Modeling Viscoelastic Wall Properties of Ovine Arteries}, ISBN={9780791848913}, url={http://dx.doi.org/10.1115/sbc2009-205640}, DOI={10.1115/sbc2009-205640}, abstractNote={Generation of a complete map of arterial wall mechanical properties can improve treatment of cardiovascular diseases via contributions to design of patient specific vascular substitutes used to alleviate atherosclerosis and stenoses, which are predominant in arterial pathways (i.e., abdominal aorta, carotids, or femoral arteries). Clinically useful estimation of arterial properties from patient data requires both efficient algorithms and models that are both complex enough to capture clinically important properties and simple enough to allow rapid computation. In this study, we used mechanical models accounting for both elastic and viscoelastic wall deformation to analyze how vessel properties and associated model parameters vary with artery type. It is known that for the aorta wall, deformation is dominated by nonlinear elastic dynamics, while for the smaller vessels (e.g. the carotid artery) deformation is dominated by viscoelastic responses. The latter is correlated with composition of the vessels; the aorta contains significantly less smooth muscle cells (∼40%) than the carotid artery (∼60%), and has significantly more elastin (see Fig 1).}, booktitle={ASME 2009 Summer Bioengineering Conference, Parts A and B}, publisher={ASME}, author={Valdez-Jasso, Daniela and Haider, Mansoor A. and Campbell, Stephen L. and Bia, Daniel and Zocalo, Yanina and Armentano, Ricardo L. and Olufsen, Mette S.}, year={2009}, month={Jun} }
 @inproceedings{ashari_nikoukhah_campbell_2009, title={Robust Multi-Model Fault Detection and Control using an Active Closed-Loop Approach}, booktitle={Proceedings of the 15th IFAC Symposium on System Identification - SYSID 2009}, author={Ashari, A.E. and Nikoukhah, R. and Campbell, S.L.}, year={2009} }
 @article{campbell_linh_2009, title={Stability criteria for differential-algebraic equations with multiple delays and their numerical solutions}, volume={208}, ISSN={["1873-5649"]}, DOI={10.1016/j.amc.2008.12.008}, abstractNote={This paper is concerned with the asymptotic stability of differential-algebraic equations with multiple delays and their numerical solutions. First, we give a sufficient condition for delay-independent stability. After characterizing the coefficient matrices that satisfy this stability condition, we propose some practical checkable criteria for asymptotic stability. Then we investigate the stability of numerical solutions obtained by θ-methods and BDF methods. Finally, solvability and stability of a class of weakly regular delay differential-algebraic equations are analyzed.}, number={2}, journal={APPLIED MATHEMATICS AND COMPUTATION}, author={Campbell, Stephen L. and Linh, Vu Hoang}, year={2009}, month={Feb}, pages={397–415} }
 @inproceedings{drake_bradshaw_violante_campbell_2009, title={Two applications of Modeling and Simulation in the Design and Development of Navy Systems}, author={Drake, Kimberly J. and Bradshaw, Kristen and Violante, Patrick and Campbell, S.L.}, year={2009}, month={May} }
 @inproceedings{andjelkovic_sweetingham_campbell_2008, title={Active fault detection in nonlinear systems using auxiliary signals}, ISBN={9781424420780}, url={http://dx.doi.org/10.1109/acc.2008.4586809}, DOI={10.1109/acc.2008.4586809}, abstractNote={In recent years active approaches for fault detection using test signals have been developed. This paper reports on progress in extending one of these approaches from linear systems to nonlinear systems. Theoretical results are presented on the use of linearizations which is based on sufficiently small nonlinearities. An optimization based approach is also presented for large nonlinearities. Examples are given.}, booktitle={2008 American Control Conference}, publisher={IEEE}, author={Andjelkovic, Ivan and Sweetingham, Kelly and Campbell, Stephen L.}, year={2008}, month={Jun} }
 @article{engelsone_campbell_2008, title={Adjoint estimation using direct transcription multipliers: compressed trapezoidal method}, volume={9}, ISSN={["1573-2924"]}, DOI={10.1007/s11081-008-9038-2}, number={3}, journal={OPTIMIZATION AND ENGINEERING}, author={Engelsone, Anna and Campbell, Stephen L.}, year={2008}, month={Sep}, pages={291–305} }
 @inproceedings{okay_campbell_kunkel_2008, title={Completions of Implicitly Defined Vector fields and their applications}, booktitle={Proceedings of the International Symposium on Mathematical Theory of Networks and Systems (MTNS 08)}, author={Okay, I. and Campbell, S.L. and Kunkel, Peter}, year={2008} }
 @article{campbell_linh_petzold_2008, title={Differential-algebraic equations}, volume={3}, ISSN={1941-6016}, url={http://dx.doi.org/10.4249/scholarpedia.2849}, DOI={10.4249/scholarpedia.2849}, abstractNote={• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.}, number={8}, journal={Scholarpedia}, publisher={Scholarpedia}, author={Campbell, Stephen and Linh, Vu and Petzold, Linda}, year={2008}, pages={2849} }
 @article{nikoukhah_campbell_2008, title={On the detection of small parameter variations in linear uncertain systems}, volume={14}, ISSN={["1435-5671"]}, DOI={10.3166/EJC.14.158-171}, abstractNote={The problem of detecting small parameter variations in linear uncertain systems, with the possibility of injecting an input signal to enhance detection, is considered. A constructive method for the construction of an optimal input signal for achieving guaranteed detection with specified precision is presented. The method is an extension of the multi-model approach used for the construction of auxiliary signals for failure detection. The application to the problem of incipient fault detection is investigated.}, number={2}, journal={EUROPEAN JOURNAL OF CONTROL}, author={Nikoukhah, Ramine and Campbell, Steve L.}, year={2008}, pages={158–171} }
 @article{choe_campbell_nikoukhah_2009, title={Optimal piecewise-constant signal design for active fault detection}, volume={82}, ISSN={["1366-5820"]}, DOI={10.1080/00207170801993587}, abstractNote={Recently there has been an increasing interest in active fault detection when traditional approaches are not effective or cannot be used. Previous papers have shown how to construct continuously varying test (auxiliary) signals for use in fault detection and identification. Such signals may not always be easy to implement. In this paper a new algorithm is presented to compute optimal piecewise constant test signals. In the important case where the test signal changes values a small number of times, the new test signals can be both smaller and more effective than test signals computed by other means. Two computational examples are given to illustrate both computational issues and differences between different types of piecewise constant signals.}, number={1}, journal={INTERNATIONAL JOURNAL OF CONTROL}, author={Choe, D. and Campbell, S. L. and Nikoukhah, R.}, year={2009}, pages={130–146} }
 @article{campbell_märz_rentrop_petzold_2006, title={Differential-Algebraic Equations}, DOI={10.4171/owr/2006/18}, abstractNote={The topic of Differential Algebraic Equations (DAEs) began to attract significant research interest in applied and numerical mathematics in the early 1980's. Today, a quarter of a century later, DAEs are an independent field of research, which is gaining in importance and becoming of increasing interest for both applications and mathematical theory.\\\ This Oberwolfach workshop brought together 48 experts in applied mathematics, among them, on the one hand, some who have already influenced and formed the developments of the field, and on the other hand, some very young researchers who have shown outstanding creativity and competence in connection with their PhD theses and thus raise great hopes for further advances.\\\ The 16 female and 32 male scientists came from 13 countries to meet and work together in the wonderful, unique Oberwolfach atmosphere, which stimulated a fruitful and pleasant collaboration.\\\ The schedule comprised a total of 34 presentations, 18 of which were arranged into 14 survey lectures (some of them with more than one speaker) offering a broader treatment of a particular subject. 16 shorter contributions supplemented the scientific programmme. The areas can be classified (of course with large overlap) into 4 groups: \begin{itemize} \item abstract differential algebraic systems, coupled systems, partial differential algebraic systems; \item analysis of (ordinary) differential algebraic equations and application of numerical methods to problems having new mathematical complexity; \item innovative and improved numerical integration methods to solve highly complex application problems; \item optimization with constraints described by DAEs and control problems concerning DAEs. \end{itemize} The broad range of these areas and the diversity of the participants stimulated fruitful discussions between the different branches and gave rise to new contacts and collaborations. A considerable gain in knowledgde and progress became obvious, which includes the formulation of open questions and challenges for the future.\\\ We are grateful to the Mathematisches Forschungsinstitut Oberwolfach for providing an inspiring setting for this workshop.}, journal={Oberwolfach Reports}, publisher={European Mathematical Publishing House}, author={Campbell, Stephen and März, Roswitha and Rentrop, Peter and Petzold, Linda}, year={2006}, pages={1077–1168} }
 @article{campbell_maerz_2007, title={Direct transcription solution of high index optimal control problems and regular Euler-Lagrange equations}, volume={202}, ISSN={["1879-1778"]}, DOI={10.1016/j.cam.2006.02.024}, abstractNote={Direct transcription methods are used to solve optimal control problems in many industrial settings. Models for physical systems often take the form of differential algebraic equations (DAEs). The index of the DAE traditionally is viewed as an important factor in deciding whether a particular numerical approach should be used. Recently it has been observed that what the user thinks is the index of the DAE may not be the same as the index available to the optimization software. An investigation of this fact is underway in order to develop guidelines to assist users of various numerical optimal control packages. This paper develops some theoretical results that will be needed for this development.}, number={2}, journal={JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS}, author={Campbell, Stephen L. and Maerz, Roswitha}, year={2007}, month={May}, pages={186–202} }
 @article{engelsone_campbell_betts_2007, title={Direct transcription solution of higher-index optimal control problems and the virtual index}, volume={57}, ISSN={["1873-5460"]}, DOI={10.1016/j.apnum.2006.03.012}, abstractNote={Direct transcription methods are a popular approach for solving optimal control problems. They are sometimes able to solve problems that the classical numerical theory would suggest that they cannot solve. The dynamics of an equality constrained optimal control problem form a differential algebraic equation (DAE), and most numerical methods for solving these optimal control problems require solving this DAE for the states and algebraic variables, which would imply that the problem is unsolvable if this DAE is high index. We will demonstrate that direct transcription methods, which use a different approach, can successfully solve some higher index equality constrained optimal control problems and that the role of the index needs reinterpretation when using direct transcription methods. These results and observations have implications for software design and guidance provided to users.}, number={3}, journal={APPLIED NUMERICAL MATHEMATICS}, author={Engelsone, A. and Campbell, S. L. and Betts, J. T.}, year={2007}, month={Mar}, pages={281–296} }
 @article{betts_campbell_engelsone_2007, title={Direct transcription solution of optimal control problems with higher order state constraints: theory vs practice}, volume={8}, ISSN={["1573-2924"]}, DOI={10.1007/s11081-007-9000-8}, number={1}, journal={OPTIMIZATION AND ENGINEERING}, author={Betts, J. T. and Campbell, S. L. and Engelsone, A.}, year={2007}, month={Mar}, pages={1–19} }
 @article{drake_campbell_andjelkovic_sweetingham_2007, title={Model-Based Failure Detection on Nonlinear Systems: Theory and Transition}, volume={119}, ISSN={0028-1425 1559-3584}, url={http://dx.doi.org/10.1111/j.0028-1425.2007.00022.x}, DOI={10.1111/j.0028-1425.2007.00022.x}, abstractNote={AbstractFailure detection is an active area of Navy research due to its many important applications. Recently, an approach for multi‐model identification and fault detection in the presence of bounded energy noise over finite time intervals has been introduced. This family of algorithms was originally designed to work on linear systems that can be modeled analytically. In this paper, efforts made toward extending this algorithm for fault detection to nonlinear systems along with efforts in testing this family of algorithms on real systems are discussed.}, number={2}, journal={Naval Engineers Journal}, publisher={Wiley}, author={Drake, Kimberly J. and Campbell, Stephen L. and Andjelkovic, Ivan and Sweetingham, Kelly}, year={2007}, month={Oct}, pages={93–107} }
 @article{campbell_betts_engelsone_nikoukhah_najafi_2007, title={Some software aspects of DAE simulation & optimization software}, volume={7}, ISSN={1617-7061 1617-7061}, url={http://dx.doi.org/10.1002/pamm.200700495}, DOI={10.1002/pamm.200700495}, abstractNote={AbstractConsiderable numerical software has been written for simulation and optimization of dynamical systems. From the beginning of their development, differential algebraic equations (DAEs) have often been proposed as a way to make modeling easier. The modeler need only write down equations relating the variables in the model. However, much DAE software requires at least as much user numerical and mathematical expertise as explicit methods. An important aspect of our research has been working toward helping the idea of DAEs achieve its promise in modeling and simulation by both pushing the software to handle more general problems and to also allow for less user expertise. Some recent examples are presented where this research impacts on software and their underlying algorithms. Space necessitates we assume the reader has a rough idea of what a DAE is. The examples are implicit Scicos, and optimization of DAE models. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)}, number={1}, journal={PAMM}, publisher={Wiley}, author={Campbell, S. L. and Betts, J. T. and Engelsone, A. and Nikoukhah, R. and Najafi, M.}, year={2007}, month={Dec}, pages={1023103–1023104} }
 @article{okay_campbell_kunkel_2007, title={The additional dynamics of least squares completions for linear differential algebraic equations}, volume={425}, ISSN={["1873-1856"]}, DOI={10.1016/j.laa.2007.02.005}, abstractNote={Several approaches have been proposed for numerically solving lower dimensional, nonlinear, higher index differential algebraic equations (DAEs) for which more classical numerical methods such as backward differentiation or implicit Runge–Kutta may not be appropriate. One of these approaches is called explicit integration (EI). This approach is based on solving nonlinear DAE derivative arrays using nonlinear singular least squares methods. This results in a computed ODE, called the least squares completion, whose solutions contain those of the original DAE. This ODE is then integrated by a classical numerical method. The additional dynamics of the least squares completion can affect the numerical solution of the DAE. This paper begins the study of determining these extra dynamics.}, number={2-3}, journal={LINEAR ALGEBRA AND ITS APPLICATIONS}, author={Okay, Irfan and Campbell, Stephen L. and Kunkel, Peter}, year={2007}, month={Sep}, pages={471–485} }
 @inproceedings{drake_campbell_andjelkovic_sweetingham_2006, title={Active Incipient Failure Detection: A Nonlinear Case Study}, booktitle={Proceedings of the 4th International Conference on Computing, Communications and Control Technologies: CCCT '06}, author={Drake, K.J. and Campbell, S.L. and Andjelkovic, I. and Sweetingham, K.}, year={2006} }
 @inproceedings{drake_campbell_andjelkovic_hannas_sweetingham_2006, title={Applications of Robust Failure Detection Algorithms to Power Systems}, ISBN={1599751747}, url={http://dx.doi.org/10.1109/isap.2005.1599275}, DOI={10.1109/isap.2005.1599275}, abstractNote={As modelling and simulation become increasingly popular in the design process and as an alternative to expensive testing, fault detection methods based on model identification algorithms become more reliable as well as less expensive and easier to implement. In this paper we discuss the application of two active fault detection algorithms based on model identification to power systems. The algorithms are similar in theory though differ in implementation. The first is a direct optimization approach that handles more general systems and more varied constraints. It requires more sophisticated software but it's easily adapted to more than two models. The second algorithm is a constrained control approach that can be implemented on common math software, such as Matlab or Scilab, and handles model uncertainty. In both cases, the algorithms are free of false alarms depending upon the quality of the models used}, booktitle={Proceedings of the 13th International Conference on, Intelligent Systems Application to Power Systems}, publisher={IEEE}, author={Drake, K.J. and Campbell, S.L. and Andjelkovic, I.V. and Hannas, B.L. and Sweetingham, K.A.}, year={2006}, month={Mar} }
 @article{nikoukhah_campbell_2006, title={Auxiliary signal design for active failure detection in uncertain linear systems with a priori information}, volume={42}, ISSN={["1873-2836"]}, DOI={10.1016/j.automatica.2005.09.011}, abstractNote={A method for auxiliary signal design for active failure detection based on a multi-model formulation of normal and failed systems is developed which allows for a priori information about initial conditions and the possibility of having a known input in addition to the test signal. These results permit the consideration of additional types of failures, such as biases, that a previous approach could not handle. Both theoretical results and computational algorithms are developed.}, number={2}, journal={AUTOMATICA}, author={Nikoukhah, R and Campbell, SL}, year={2006}, month={Feb}, pages={219–228} }
 @inproceedings{choe_campbell_nikoukhah_2006, title={Comparison between failure detection test signals for continuous systems and sampled-data systems}, ISBN={1424401712}, url={http://dx.doi.org/10.1109/cdc.2006.377349}, DOI={10.1109/cdc.2006.377349}, abstractNote={In active failure detection it is essential to have auxiliary signal inputs that are capable of identifying the status of observed systems while the operations of the systems are minimally disturbed by the extra input. Recently, two signal-design-algorithms for active failure detection were introduced: one that computes optimal continuous detection signals for continuous systems (CS) and the other that designs optimal piecewise-constant signal inputs for sampled-data systems (SDS). In some applications simple piecewise constant inputs are sought. In this paper, we combine the key ideas of the two previous algorithms and present an algorithm that finds optimal piecewise-constant signals for continuous systems. This modified algorithm provides a suboptimal detection signal inputs for continuous systems and would appear to be greatly faster than the original CS algorithm. We also compare the three algorithms and the corresponding optimal signals through a computational experiment}, booktitle={Proceedings of the 45th IEEE Conference on Decision and Control}, publisher={IEEE}, author={Choe, D. and Campbell, S. L. and Nikoukhah, R.}, year={2006} }
 @inproceedings{campbell_drake_andjelkovic_sweetingham_choe_2006, title={Model Based Failure Detection using Test Signals from Linearizations: A Case Study}, ISBN={0780397975}, url={http://dx.doi.org/10.1109/cacsd.2006.285526}, DOI={10.1109/cacsd.2006.285526}, booktitle={2006 IEEE Conference on Computer-Aided Control Systems Design}, publisher={IEEE}, author={Campbell, S. and Drake, K. and Andjelkovic, I. and Sweetingham, K. and Choe, D.}, year={2006}, month={Oct} }
 @book{campbell_chancelier_nikoukhah_2006, title={Modeling and simulation in Scilab/Scicos}, ISBN={0387278028}, publisher={New York: Springer}, author={Campbell, S. and Chancelier, J.-P. and Nikoukhah, R.}, year={2006} }
 @inproceedings{engelsone_campbell_betts_2006, title={Order of Convergence in the Direct Transcription Solution of Optimal Control Problems}, ISBN={0780395670}, url={http://dx.doi.org/10.1109/cdc.2005.1582741}, DOI={10.1109/cdc.2005.1582741}, abstractNote={In the direct transcription approach to the numerical solution of optimal control problems, the optimal control problem is discretized and the resulting nonlinear programming problem is solved numerically. There has been considerable study over the last 10 years on order of convergence of cost, state, multipliers, and control. This paper discusses these questions, and the highly technical results in the literature, in the context of their implications for industrial grade optimal control packages.}, booktitle={Proceedings of the 44th IEEE Conference on Decision and Control}, publisher={IEEE}, author={Engelsone, A. and Campbell, S.L. and Betts, J.T.}, year={2006}, month={Oct} }
 @inproceedings{nikoukhah_campbell_2006, title={Robust detection of incipient faults: an active approach}, ISBN={0978672011 0978672003}, url={http://dx.doi.org/10.1109/med.2006.328694}, DOI={10.1109/med.2006.328694}, abstractNote={The methodology of auxiliary signal design for robust failure detection based on multi-model formulation of normal and failed systems is used to study the problem of incipient fault detection. Here, the fault is modeled as a drift in a system parameter, and an auxiliary signal is to be designed to enhance the detection of variations in this parameter. It is shown that it is possible to consider the model of the system with a drifted parameter as a second model and use the multi-model framework for designing the auxiliary signal by considering the limiting case as the parameter variation goes to zero. The result can be applied very effectively to early detection problems where small parameter variations should be detected}, booktitle={2006 14th Mediterranean Conference on Control and Automation}, publisher={IEEE}, author={Nikoukhah, R. and Campbell, S. L.}, year={2006}, month={Jun} }
 @inproceedings{choe_campbell_nikoukhah_2005, title={A comparison of optimal and suboptimal auxiliary signal design approaches for robust failure detection}, ISBN={0780393546}, url={http://dx.doi.org/10.1109/cca.2005.1507340}, DOI={10.1109/cca.2005.1507340}, abstractNote={Recently a new approach for multi-model identification and failure detection in the presence of model uncertainty and bounded energy noise over finite time intervals was introduced. This approach involved offline computation of an auxiliary signal and online application of the detection and identification test. The theory and algorithms include optimization over a parameter beta. By considering a modification of the original problem it is possible to avoid this parameter and solve a related but different problem which is more of a standard robust control problem. This modification provides a suboptimal solution of the original problem and would appear to greatly speed up the algorithms. This paper provides the first examination of the effect of ignoring the parameter beta. We provide examples showing that the more usual robust control approach cannot solve some problems that the new approach can. We also provide insight into when the simpler algorithm can be used and what is the cost in doing so}, booktitle={Proceedings of 2005 IEEE Conference on Control Applications, 2005. CCA 2005.}, publisher={IEEE}, author={Choe, D. and Campbell, Stephen L. and Nikoukhah, R.}, year={2005}, month={Sep} }
 @article{nikoukhah_campbell_2005, title={A multi-model approach to failure detection in uncertain sampled-data systems}, volume={11}, ISSN={["0947-3580"]}, DOI={10.3166/ejc.11.255-265}, abstractNote={In this paper we propose a methodology for active failure detection for sampled-data systems in the presence of model uncertainty. Active failure detection consists of injecting a signal (called an auxiliary signal) into the system. Using a multi-model framework to represent normal and failed behaviors of the system,we develop algorithms for the design of optimal auxiliary signals and online detection tests. The tests give guaranteed detection. Any conservatism inherited from the multi-model framework increases the size of the test signal and is not reflected in missed failures or false alarms as with several other approaches.}, number={3}, journal={EUROPEAN JOURNAL OF CONTROL}, author={Nikoukhah, R and Campbell, SL}, year={2005}, pages={255–265} }
 @inproceedings{choe_campbell_nikoukhah_2005, title={Auxiliary Signal Design for Robust Failure Detection: A Case Study}, ISBN={0780391373}, url={http://dx.doi.org/10.1109/icca.2005.1528269}, DOI={10.1109/icca.2005.1528269}, abstractNote={Recently an approach for multi-model identification and failure detection in the presence of model uncertainty and bounded energy noise over finite time intervals was introduced. This approach involved offline computation of an auxiliary signal and online application of the detection and identification test software has been developed to carry out this approach. This paper provides the first careful case study investigating a number of issues related to use of this software. Guidelines for users and suggestions for improvement are presented.}, booktitle={2005 International Conference on Control and Automation}, publisher={IEEE}, author={Choe, D. and Campbell, S.L. and Nikoukhah, R.}, year={2005}, month={Nov} }
 @inproceedings{najafi_nikoukhah_campbell_2005, title={Computation of consistent initial conditions for multi-mode DAEs: application to Scicos}, ISBN={0780386361}, url={http://dx.doi.org/10.1109/cacsd.2004.1393863}, DOI={10.1109/cacsd.2004.1393863}, abstractNote={Scicos, which can simulate hybrid systems, has been extended to include some types of implicit models. This results in multi-mode DAEs. Switching from one model to another requires robust and efficient reinitialization. This paper discusses some of the special problems faced in the simulation of multi-model DAEs and proposes two solutions for finding consistent initial conditions. These methods are designed to take advantage of the data and algorithms available in Scicos}, booktitle={2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508)}, publisher={IEEE}, author={Najafi, M. and Nikoukhah, R. and Campbell, S.L.}, year={2005}, month={Mar} }
 @inproceedings{engelsone_campbell_betts_2005, place={Villeneuve d'Ascq}, title={Direct Transcription Solution of Higher-Index Optimal Control Problems}, booktitle={17th IMACS world congress on scientific computation, applied mathematics and simulation: Paris, France, July 11-15, 2005}, publisher={École centrale de Lille}, author={Engelsone, A. and Campbell, S.L. and Betts, J.T.}, editor={Dangoumau, Nathalie and Benrejeb, Mohamed and Borne, PierreEditors}, year={2005} }
 @inbook{betts_campbell_2005, place={Philadelphia}, title={Discretize then Optimize}, ISBN={9780898715989}, booktitle={Mathematics for industry : challenges and frontiers : a process view: practice and theory}, publisher={SIAM Publications}, author={Betts, J.T. and Campbell, S.L.}, editor={Ferguson, D.R. and Peters, T.J.Editors}, year={2005} }
 @inproceedings{campbell_nikoukhah_von wissel_1994, title={Numerically generated path stabilizing controllers. I. Theoretical concerns}, ISBN={0780317831}, url={http://dx.doi.org/10.1109/acc.1994.752408}, DOI={10.1109/acc.1994.752408}, abstractNote={A method for the prescribed path control of robotic arms has previously been proposed which utilizes the ability to numerically integrate higher index DAE models quickly. In this paper the authors examine some of the issues involved with this method in order to effectively apply it to a wider class of path control problems.}, booktitle={Proceedings of 1994 American Control Conference - ACC '94}, publisher={IEEE}, author={Campbell, S.L. and Nikoukhah, R. and von Wissel, D.}, year={1994} }
 @inproceedings{najafi_nikoukhah_campbell_2005, place={Villeneuve d'Ascq}, title={The role of model formulation in DAE integration: Experience gained in developing Scicos}, booktitle={17th IMACS world congress on scientific computation, applied mathematics and simulation: Paris, France, July 11-15, 2005}, publisher={École centrale de Lille}, author={Najafi, M. and Nikoukhah, R. and Campbell, S.L.}, editor={Dangoumau, N. and Benrejeb, M. and Borne, P.Editors}, year={2005} }
 @inproceedings{campbell_selva_arevalo_2004, title={A numerical integrator for simulation of unstructured implicit models}, ISBN={0780383354}, url={http://dx.doi.org/10.23919/acc.2004.1384754}, DOI={10.23919/acc.2004.1384754}, abstractNote={Object oriented modeling naturally leads to implicitly defined dynamical systems or, as they are also called, differential algebraic equations (DAEs). Most existing DAE integrators require the equations defining the dynamical system to have a special structure. Progress on the development of a new integrator for general unstructured DAEs is presented. The new integrator is called UCP. Computational tests are given to show that the new method can successfully integrate problems that other methods have trouble with.}, booktitle={Proceedings of the 2004 American Control Conference}, publisher={IEEE}, author={Campbell, S.L. and Selva, M. and Arevalo, C.}, year={2004} }
 @inproceedings{campbell_drake_nikoukhah_2004, title={Analysis of spline based auxiliary signal design for failure detection in delay systems}, ISBN={0780379527}, url={http://dx.doi.org/10.1109/icsmc.2003.1244267}, DOI={10.1109/icsmc.2003.1244267}, abstractNote={In an active approach for model detection and its use in failure detection, an auxiliary control is applied in order to assist in model identification. An active approach for robust multi-model identification and failure detection in the presence of disturbances over possibly short time intervals has been introduced. Previous papers extended the original design procedure to problems with several delays and additive noise. The infinite dimensional delay problem was approximated by a finite dimensional system without delays and numerical examples were worked. The numerical examples seemed to converge better than was expected. In this paper we explain that convergence. In addition we discuss the extension of the previous results for delay systems with additive noise to those with small model uncertainties and explain why this additional assumption of small uncertainty, which was not present in the case without delays, is now needed for the analysis.}, booktitle={SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483)}, publisher={IEEE}, author={Campbell, SL and Drake, K. and Nikoukhah, R.}, year={2004}, month={May} }
 @book{campbell_nikoukhah_2004, title={Auxiliary Signal Design for Failure Detection}, ISBN={0691099871}, DOI={10.1515/9781400880041}, abstractNote={University Press. All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher, except for reading and browsing via the World Wide Web. Users are not permitted to mount this file on any network servers. In this book, we study the problem of active failure detection in dynamical systems. Failure detection in some form is now part of essentially every complex device or process. In some applications the detection of failures, such as water losses in nuclear reactors or engine problems on an aircraft, is important for safety purposes. The detection of failure leads to emergency actions by operators or computers and results in a quick and controlled shutdown of the system. In other situations, such as on space missions, the detection of failures results in the use of backup or alternative systems. These are the more dramatic examples and are often what one first thinks of when hearing of a failure. But in today's society failure detection also plays a fundamental role in managing costs, promoting efficiency, and protecting the environment. It is often much more economical to repair a part during a scheduled maintenance than to have a breakdown in the field. For example, failure may mean that a part or subsystem is not performing to specification, resulting in increased fuel consumption. Detecting this failure means that a scheduled repair can be made with savings of both resources and money. Failure can also mean that a part or subsystem is not performing as expected and that if allowed to continue the result could be a catastrophic failure. But again detection of this type of failure means that repairs can be initiated in an economical and convenient manner. It is much easier to repair a weakened pump than to have to clean up a major sewage spill. A number of specific examples from applications are in the cited literature. In chapters 2 and 3 we shall use a couple of intuitive examples to motivate some of the ideas that follow. Simpler academic examples will be used to illustrate most of the key ideas and algorithms. Then in the later chapters we shall include some more detailed examples from application areas. Because of the fundamental role that failure detection plays, it has been the subject of …}, publisher={Princeton University Press}, author={Campbell, Stephen L. and Nikoukhah, Ramine}, year={2004}, month={Jan} }
 @book{characterization and computation of a "good control"_2004, DOI={10.18452/2583}, abstractNote={Models for physical systems often take the form of implicit or behavioral models. One important problem is the identification of which combinations of variables are good candidtates for control variables. This paper first provides one solution to this problem for linear time varying systems. The solution is shown to be related to a general optimization problem. It is then shown how these same algorithms can be extended to a large and important class of nonlinear systems.}, journal={Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik}, year={2004}, month={May} }
 @inproceedings{drake_campbell_2004, title={Design of a Detection Signal for Fault Detection and Model Identification on Systems with Multiple Delays}, booktitle={Proceedings of the American Society of Naval Engineers Day 2004}, author={Drake, K. and Campbell, S.L.}, year={2004}, month={Jun} }
 @inproceedings{betts_campbell_engelsone_2004, title={Direct transcription solution of inequality constrained optimal control problems}, ISBN={0780383354}, url={http://dx.doi.org/10.23919/acc.2004.1386809}, DOI={10.23919/acc.2004.1386809}, abstractNote={Direct transcription is a popular way to solve the complex optimal control problems that arise in industry. With a direct transcription approach, the problem is fully discretized and then the discrete problem is solved numerically. Recently, it has been shown that the theory for direct transcription differs in several key ways from the theory for other approaches. These differences have implications for numerical algorithms and the interpretation of solutions to practical problems. This paper examines some of those differences.}, booktitle={Proceedings of the 2004 American Control Conference}, publisher={IEEE}, author={Betts, J.T. and Campbell, S.L. and Engelsone, A.}, year={2004} }
 @inproceedings{betts_campbell_kalla_2004, title={Initialization of direct transcription optimal control software}, ISBN={0780379241}, url={http://dx.doi.org/10.1109/cdc.2003.1271741}, DOI={10.1109/cdc.2003.1271741}, abstractNote={Direct transcription optimal control codes have been very successful. One common source of numerical difficulty is getting a feasible solution on the first iteration. Overcoming this often requires a high level of expertise on the user's part. This paper discusses research aimed at the development of a collection of utilities to assist users in solving complex industrial optimal control problems with direct transcription codes.}, booktitle={42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)}, publisher={IEEE}, author={Betts, J.T. and Campbell, S.L. and Kalla, N.N.}, year={2004}, month={Apr} }
 @inproceedings{najafi_nikoukhah_campbell_2004, place={Anaheim, California}, title={ODE and DAE integrators in Scicos environment}, ISBN={0889863970 9780889863972}, booktitle={Proceedings of the IASTED International Conference on Applied Simulation and Modelling and Simulation : June 28-30, 2004, Rhodes, Greece}, publisher={ACTA Press}, author={Najafi, M. and Nikoukhah, R. and Campbell, S.L.}, editor={Hamza, M.H.Editor}, year={2004} }
 @article{campbell_2004, title={Practical methods for optimal control using nonlinear programming, John T. Betts, SIAM, Philadelphia, PA, 2001, ISBN 0-89871-488-5}, volume={14}, ISSN={1049-8923 1099-1239}, url={http://dx.doi.org/10.1002/rnc.874}, DOI={10.1002/rnc.874}, abstractNote={International Journal of Robust and Nonlinear ControlVolume 14, Issue 11 p. 1019-1021 Book ReviewFree Access Practical methods for optimal control using nonlinear programming, John T. Betts, SIAM, Philadelphia, PA, 2001, ISBN 0-89871-488-5 Stephen L. Campbell, Stephen L. Campbell slc@math.ncsu.edu Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, U.S.A.Search for more papers by this author Stephen L. Campbell, Stephen L. Campbell slc@math.ncsu.edu Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, U.S.A.Search for more papers by this author First published: 11 June 2004 https://doi.org/10.1002/rnc.874AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume14, Issue11Special Issue: Robust control design from data: direct and model-based approaches25 July 2004Pages 1019-1021 ReferencesRelatedInformation}, number={11}, journal={International Journal of Robust and Nonlinear Control}, publisher={Wiley}, author={Campbell, Stephen L.}, year={2004}, month={Jun}, pages={1019–1021} }
 @inproceedings{campbell_nikoukhah_2004, title={Software for auxiliary signal design}, ISBN={0780383354}, url={http://dx.doi.org/10.23919/acc.2004.1384004}, DOI={10.23919/acc.2004.1384004}, abstractNote={An approach for multi-model identification and failure detection in the presence of model uncertainty and bounded energy noise over finite time intervals has been introduced in the literature. This approach involved offline computation of an auxiliary signal and online application of a hyperplane test. This paper discusses progress in developing a software package to carry out this procedure.}, booktitle={Proceedings of the 2004 American Control Conference}, publisher={IEEE}, author={Campbell, S.L. and Nikoukhah, R.}, year={2004} }
 @article{arevalo_campbell_selva_2004, title={Unitary partitioning in general constraint preserving DAE integrators}, volume={40}, ISSN={["0895-7177"]}, DOI={10.1016/j.mcm.2005.01.018}, abstractNote={A number of numerical algorithms have been developed for various special classes of DAEs. This paper describes a new variable step size, constraint preserving integrator for general nonlinear fully implicit higher index DAEs. Numerical implementation issues are discussed. Numerical examples illustrate the effectiveness of the new method.}, number={11-12}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Arevalo, C and Campbell, SL and Selva, M}, year={2004}, month={Dec}, pages={1273–1284} }
 @inproceedings{campbell_1988, title={A general method for nonlinear descriptor systems: an example from robotic path control}, url={http://dx.doi.org/10.1109/cdc.1988.194386}, DOI={10.1109/cdc.1988.194386}, abstractNote={Several techniques for analyzing descriptor systems by utilizing information in derivative arrays have been proposed. The author considers their application to a descriptor system arising in robotic path control. Computational speedup, attainable accuracy, and other numerical considerations are examined.<<ETX>>}, booktitle={Proceedings of the 27th IEEE Conference on Decision and Control}, publisher={IEEE}, author={Campbell, S.L.}, year={1988}, month={Jan} }
 @inproceedings{nikoukhah_campbell_2003, title={Auxiliary signal design for failure detection in uncertain sampled-data systems}, ISBN={9783952417379}, url={http://dx.doi.org/10.23919/ecc.2003.7085087}, DOI={10.23919/ecc.2003.7085087}, abstractNote={In this paper the normal and the failed behaviors of a sampleddata system are modeled using two distinct uncertain models. A proper auxiliary signal is an input signal for which the behaviors of the two systems do not intersect making guaranteed failure detection possible. Algorithms for the design of optimal proper auxiliary signals are developed.}, booktitle={2003 European Control Conference (ECC)}, publisher={IEEE}, author={Nikoukhah, R. and Campbell, S. L.}, year={2003}, month={Sep} }
 @article{nikoukhah_campbell_2003, title={Auxiliary signal design for robust active failure detection: the general cost case}, journal={Proc. Safeprocess 2003}, author={Nikoukhah, R. and Campbell, S.L.}, year={2003}, pages={259–264} }
 @inproceedings{campbell_drake_nikoukhah_2003, title={Early decision making when using proper auxiliary signals}, ISBN={0780375165}, url={http://dx.doi.org/10.1109/cdc.2002.1184790}, DOI={10.1109/cdc.2002.1184790}, abstractNote={Recently an approach for multi-model identification and failure detection in the presence of bounded energy noise over finite time intervals has been introduced. This approach involved offline computation of an auxiliary signal and online application of a hyperplane test. This approach has several advantages but as presented, observation over the full time interval was required before a decision could be made. In this paper it is shown how to modify this approach to permit early decision making with the hyperplane test.}, booktitle={Proceedings of the 41st IEEE Conference on Decision and Control, 2002.}, publisher={IEEE}, author={Campbell, S.L. and Drake, K. and Nikoukhah, R.}, year={2003}, month={Aug} }
 @inproceedings{campbell_delebecque_von wissel_1996, title={A mixed symbolic-numeric software environment}, ISBN={0780330323}, url={http://dx.doi.org/10.1109/cacsd.1996.555331}, DOI={10.1109/cacsd.1996.555331}, abstractNote={This paper presents two nonlinear examples of mechanical systems. The first example is a simple inverted pendulum, the second example is a simplified bicycle model. In Maple, using the Euler Lagrange equations, we compute the equations of motion. We have shown how to use the interface to transfer the equations to Scilab for simulation or control. We have shown that for dealing with complex models, we need the full power of Maple to perform change of variables which cannot be automatized since they require a deep a priori knowledge of the model.}, booktitle={Proceedings of Joint Conference on Control Applications Intelligent Control and Computer Aided Control System Design}, publisher={IEEE}, author={Campbell, S.L. and Delebecque, F. and von Wissel, D.}, year={1996} }
 @inproceedings{nikoukhah_campbell_2002, place={Lisbon, Portugal}, title={Active failure detection: Auxiliary signal design and on-line detection}, booktitle={MED2002 : 10th IEEE Mediterranean conference on control and automation : Instituto Superior Técnico : July 9-12, 2002 : Lisboa, Portugal : proceedings}, publisher={Institute for Systems and Robotics}, author={Nikoukhah, R. and Campbell, S.L.}, year={2002} }
 @article{campbell_drake_nikoukhah_2002, place={Lisbon, Portugal}, title={Auxiliary signal design for multi-model identification in systems with multiple delays}, journal={MED2002 : 10th IEEE Mediterranean conference on control and automation : Instituto Superior Técnico : July 9-12, 2002 : Lisboa, Portugal : proceedings}, publisher={Institute for Systems and Robotics}, author={Campbell, S.L. and Drake, K. and Nikoukhah, R.}, year={2002} }
 @article{campbell_horton_nikoukhah_2002, title={Auxiliary signal design for rapid multi-model identification using optimization}, volume={38}, ISSN={["0005-1098"]}, DOI={10.1016/S0005-1098(02)00040-7}, abstractNote={Under the assumption that one of several given models is the real underlying model of the system, a proper auxiliary signal is defined as an input signal that allows one to select the correct model. It is assumed that there is no knowledge prior to the beginning of the application of the auxiliary signal and that detection is to be done within a specified detection horizon. Under the assumption that the noise energy is bounded, a method for the computation of the minimal energy auxiliary signal is given. The new algorithm extends previous work in that it can handle more than two models and certain types of nonlinearities.}, number={8}, journal={AUTOMATICA}, author={Campbell, SL and Horton, KG and Nikoukhah, R}, year={2002}, month={Aug}, pages={1313–1325} }
 @article{nikoukhah_campbell_horton_delebecque_2002, title={Auxiliary signal design for robust multimodel identification}, volume={47}, DOI={10.1109/9.981737}, abstractNote={Under the assumption that one of two given linear models is the real underlying model of the system, a proper auxiliary signal is defined as an input signal that allows the selection of the correct model. Under the assumption that model noises have bounded energy, the separability index is defined as the inverse of the energy of the proper auxiliary signal of least energy. A method for the computation of this index and the construction of the auxiliary signal is presented. Finally, an efficient procedure for online identification, called the "hyperplane test", is developed.}, number={1}, journal={IEEE Transactions on Automatic Control}, author={Nikoukhah, R. and Campbell, Stephen and Horton, K. G. and Delebecque, F.}, year={2002}, pages={158–164} }
 @article{betts_biehn_campbell_huffman_2002, title={Compensating for order variation in mesh refinement for direct transcription methods II: Computational experience}, volume={143}, ISSN={["0377-0427"]}, DOI={10.1016/S0377-0427(01)00509-X}, abstractNote={The numerical theory for Implicit Runge Kutta methods shows that there can be order reduction when these methods are applied to either stiff or differential algebraic equations. A previous paper introduced a way to try and compensate for this order reduction in designing mesh refinement strategies. This paper presents the results from a number of computational studies on the effectiveness of this approach. In addition, we present a new test problem which can be used to examine the efficiency of codes developed for a particular class of applications.}, number={2}, journal={JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS}, author={Betts, JT and Biehn, N and Campbell, SL and Huffman, WP}, year={2002}, month={Jun}, pages={237–261} }
 @article{betts_biehn_campbell_2002, title={Convergence of nonconvergent IRK discretizations of optimal control problems with state inequality constraints}, volume={23}, ISSN={["1095-7197"]}, DOI={10.1137/S1064827500383044}, abstractNote={It has been observed that optimization codes are sometimes able to solve inequality state constrained optimal control problems with discretizations which do not converge when used as integrators on the constrained dynamics. Understanding this phenomenon could lead to a more robust design for direct transcription codes as well as better test problems. This paper examines how this phenomenon can occur. The difference between solving index 3 differential algebraic equations (DAEs) using the trapezoid method in the context of direct transcription for optimal control problems and a straightforward implicit Runge--Kutta (IRK) formulation of the same trapezoidal discretization is analyzed. It is shown through numerical experience and theory that the two can differ as much as O(1/h3) in the control. The optimization can use a small sacrifice in the accuracy of the states in the early stages of the trapezoidal method to produce better accuracy in the control, whereas more precise solutions converge to an incorrect solution. Convergence independent of the index of the constraints is then proven for one class of problems. The theoretical results are used to explain computational observations.}, number={6}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Betts, JT and Biehn, N and Campbell, SL}, year={2002}, month={May}, pages={1981–2007} }
 @inproceedings{campbell_terrell_2002, place={Raleigh, NC}, title={Determining flatness for complex nonlinear systems}, ISBN={0780326423}, url={http://dx.doi.org/10.1109/secon.1995.513069}, DOI={10.1109/secon.1995.513069}, abstractNote={Fliess et al. (1992, 1993) developed the concept of a flat system and showed how it can be useful in the construction of nonlinear controllers. For large complex systems of possibly high relative degree the checking of flatness may be difficult and time consuming. The present authors show how it is possible to quickly check numerically for flatness even for complex implicitly formulated nonlinear systems.}, booktitle={Proceedings IEEE Southeastcon '95. Visualize the Future}, publisher={IEEE}, author={Campbell, S.L. and Terrell, W.J.}, year={2002}, month={Nov}, pages={118–122} }
 @inbook{campbell_1998, title={Intelligent DAE solvers and user friendly design, simulation, and analysis packages}, DOI={10.1109/icsmc.1998.726491}, abstractNote={Simulation and design packages are an integral part of many computational systems. However, the current capabilities of many of these systems are limited by their ability to handle naturally posed questions in a user friendly manner. This paper examines what would be required to handle those problems that naturally lead to differential algebraic equations.}, booktitle={1998 IEEE International Conference on Systems, Man, and Cybernetics: Intelligent systems for humans in a cyberworld, Hyatt La Jolla, San Diego, California, USA, October 11-14, 1998}, publisher={Piscataway, NJ: IEEE}, author={Campbell, Stephen}, year={1998}, pages={177–3182} }
 @inbook{biehn_campbell_delebecque_nikoukhah_1998, title={Observer design for linear time varying descriptor systems: Numerical algorithms}, DOI={10.1109/cdc.1998.761815}, abstractNote={Examines the design of observers for linear time varying descriptor systems for which the observer estimates are also physically correct in that they satisfy the same constraints as the solutions of the descriptor system. Careful attention is paid to ensuring that all quantities are computable by numerical algorithms. One way to implement this approach is fully developed. A computational example is given.}, booktitle={Proceedings of the 37th IEEE Conference on Decision and Control: December 16-18, 1998, Hyatt Regency Westshore, Tampa, Florida}, publisher={Piscataway, N.J.: IEEE}, author={Biehn, N. and Campbell, Stephen and Delebecque, F. and Nikoukhah, R.}, year={1998}, pages={3801–3806} }
 @inproceedings{von wissel_nikoukhah_campbell_1994, title={On a new predictive control strategy: application to a flexible-joint robot}, ISBN={0780319680}, url={http://dx.doi.org/10.1109/cdc.1994.411325}, DOI={10.1109/cdc.1994.411325}, abstractNote={It is shown that it is possible to greatly improve the performance of the predictive control strategy proposed by Jankowski and Van Brussel (1992) by using preliminary linear feedback. This is illustrated using the example of a flexible-joint robot path following problem.<<ETX>>}, booktitle={Proceedings of 1994 33rd IEEE Conference on Decision and Control}, publisher={IEEE}, author={von Wissel, D. and Nikoukhah, R. and Campbell, S.L.}, year={1994} }
 @article{campbell_horton_nikoukhah_delebecque_2002, title={Optimization formulations of auxiliary signal design for rapid multi-model identification}, volume={38}, journal={Automatica}, author={Campbell, S.L. and Horton, K. and Nikoukhah, R. and Delebecque, F.}, year={2002}, pages={1313–1325} }
 @inproceedings{campbell_nikoukhah_2002, title={The design of auxiliary signals for robust active failure detection in uncertain systems}, booktitle={Proceedings of the Mathematical Theory of Networks and Systems}, author={Campbell, S.L. and Nikoukhah, R.}, year={2002} }
 @inproceedings{nikoukhah_campbell_delebecque_2001, title={Auxiliary signal design for failure detection in uncertain systems}, booktitle={Proceedings of the 9th IEEE Mediterranean Conference on Control and Automation}, publisher={Piscataway, N.J.: IEEE}, author={Nikoukhah, R. and Campbell, S.L. and Delebecque, F.}, editor={P. P. Groumpos, N. T. Koussoulas and Polycarpou, M.Editors}, year={2001} }
 @article{campbell_2001, title={Numerical analysis and systems theory}, volume={11}, number={5}, journal={International Journal of Applied Mathematics and Computer Science}, author={Campbell, S. L.}, year={2001}, pages={1025–1033} }
 @article{biehn_campbell_nikoukhah_delebecque_2001, title={Numerically constructible observers for linear time-varying descriptor systems}, volume={37}, ISSN={["0005-1098"]}, DOI={10.1016/S0005-1098(00)00168-0}, abstractNote={This paper examines the design of observers for linear time-varying descriptor systems. An observer is designed for which the observer estimates are also physically correct in that they satisfy the same constraints as the solutions of the descriptor system. Careful attention is paid to ensuring that all quantities are computable by numerical algorithms. One way to implement this approach is fully developed. A computational example is given.}, number={3}, journal={AUTOMATICA}, author={Biehn, N and Campbell, SL and Nikoukhah, R and Delebecque, F}, year={2001}, month={Mar}, pages={445–452} }
 @inproceedings{campbell_drake_nikoukhah_delebecque_2001, title={Rapid multi-model identification in systems with delay}, booktitle={Time delay systems 2001 (TDS 2001): A proceedings volume from the 3rd IFAC Workshop, Sante Fe, New Mexico, USA, 8-10 December 2001}, publisher={Oxford: Pergamon}, author={Campbell, S.L. and Drake, K. and Nikoukhah, R. and Delebecque, F.}, editor={K. Gu, C. T. Abdallah and Niculescu, S.-I.Editors}, year={2001}, pages={296–301} }
 @article{betts_biehn_campbell_huffman_2000, title={Compensating for order variation in mesh refinement for direct transcription methods}, volume={125}, ISSN={["0377-0427"]}, DOI={10.1016/S0377-0427(00)00465-9}, abstractNote={The numerical theory for Implicit Runge–Kutta methods shows that there can be order reduction when these methods are applied to either stiff or differential algebraic equations. This paper discusses how this theory can be utilized in direct transcription trajectory optimization by modifying a currently used mesh refinement strategy.}, number={1-2}, journal={JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS}, author={Betts, JT and Biehn, N and Campbell, SL and Huffman, WP}, year={2000}, month={Dec}, pages={147–158} }
 @inproceedings{betts_biehn_campbell_huffman_2000, title={Computational experience with exploiting order variation in mesh refinement for direct transcription methods}, booktitle={Proceedings: 16th IMACS World Congress.}, publisher={New Brunswick, NJ: IMACS}, author={Betts, J. T. and Biehn, N. and Campbell, S. L. and Huffman, W.P.}, year={2000} }
 @inproceedings{betts_biehn_campbell_huffman_2000, title={Convergence of nonconvergent IRK discretizations of optimal control problems}, booktitle={Proceedings: 16th IMACS World Congress.}, publisher={New Brunswick, NJ: IMACS}, author={Betts, J. T. and Biehn, N. and Campbell, S. L. and Huffman, W.P.}, year={2000} }
 @article{nikoukhah_campbell_delebecque_2000, title={Detection signal design for failure detection: a robust approach}, volume={14}, ISSN={["0890-6327"]}, DOI={10.1002/1099-1115(200011)14:7<701::AID-ACS617>3.0.CO;2-6}, abstractNote={HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Detection Signal Design for Failure Detection: a Robust Approach Ramine Nikoukhah, Stephen L. Campbell, François Delebecque}, number={7}, journal={INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING}, author={Nikoukhah, R and Campbell, SL and Delebecque, F}, year={2000}, month={Nov}, pages={701–724} }
 @inproceedings{nikoukhah_delebecque_campbell_horton_2000, title={Multi-model identification and the separability index}, number={2000}, booktitle={Proceedings of Mathematical Theory of Networks and Systems, 2000}, author={Nikoukhah, R. and Delebecque, F. and Campbell, S.L. and Horton, K.}, year={2000} }
 @inproceedings{nikoukhah_campbell_delebecque_2000, title={On a general descriptor LQ problem}, booktitle={Proceedings of the 8th IEEE Mediterranean Conference on Control & Automation: July 17-19, 2000, University of Patras, Patras, Greece.}, author={Nikoukhah, R. and Campbell, S. L. and Delebecque, F.}, year={2000} }
 @article{riaza_campbell_marszalek_2000, title={On singular equilibria of index-1 DAEs}, volume={19}, ISSN={["0278-081X"]}, DOI={10.1007/BF01212467}, number={2}, journal={CIRCUITS SYSTEMS AND SIGNAL PROCESSING}, author={Riaza, R and Campbell, SL and Marszalek, W}, year={2000}, pages={131–157} }
 @inproceedings{campbell_horton_nikoukhah_delebecque_2000, title={Rapid model selection and the separability index}, DOI={10.1016/s1474-6670(17)37517-1}, abstractNote={Under the assumption that one of two given models is the real underlying model of the system, a proper auxiliary signal is defined as an input signal that allows one to select the correct model. It is assumed that there is no knowledge prior to the beginning of the application of the auxiliary signal and that detection is to be done within a specified detection horizon. Under the assumption that the noise energy is bounded, the separability index is defined as the least energy of a proper auxiliary signal. A method for computation of this index is presented.}, booktitle={Fault detection, supervision and safety for technical processes 2000 (SAFEPROCESS 2000): A proceedings volume from the 4th IFAC Symposium, Budapest, Hungary, 14-16 June 2000}, publisher={Oxford, UK; New York: Published for the  International Federation of Automatic Control by Pergamon}, author={Campbell, Stephen and Horton, K. and Nikoukhah, R. and Delebecque, F.}, year={2000}, pages={1187–1192} }
 @article{biehn_campbell_jay_westbrook_2000, title={Some comments on DAE theory for IRK methods and trajectory optimization}, volume={120}, ISSN={["0377-0427"]}, DOI={10.1016/S0377-0427(00)00306-X}, abstractNote={It has been observed elsewhere in the literature that the activation of constraints in a trajectory optimization problem can lead to higher index DAEs. Several existing codes can handle a number of these constrained problems. In this note we will discuss why the situation is more complex than just saying a higher index DAE occurs. The discussion is in the context of a specific industrial code SOCS but the observations made here have relevance for a number of methods and have implications for what types of test problems a code should be tested on.}, number={1-2}, journal={JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS}, author={Biehn, N and Campbell, SL and Jay, L and Westbrook, T}, year={2000}, month={Aug}, pages={109–131} }
 @article{zou_campbell_2000, title={The jump behavior and stability analysis for 2-D descriptor systems}, volume={11}, DOI={10.1023/a:1008429611994}, number={4}, journal={Multidimensional Systems and Signal Processing}, author={Zou, Y. and Campbell, S.L.}, year={2000}, pages={339–358} }
 @article{marszalek_campbell_1999, title={DAEs arising from traveling wave solutions of PDEs II}, volume={37}, ISSN={["0898-1221"]}, DOI={10.1016/S0898-1221(98)00238-7}, abstractNote={The study of traveling wave solutions of PDEs sometimes leads to systems of Differential Algebraic Equations (DAEs). This paper examines a family of DAEs that arise in this manner from the Magnetohydrodynamics (MHD) equations. These DAEs are of interest in their own right, as a source of test problems for DAE numerical integrators, and because of their relationship to the MHD equations.}, number={1}, journal={COMPUTERS & MATHEMATICS WITH APPLICATIONS}, author={Marszalek, W and Campbell, SL}, year={1999}, month={Jan}, pages={15–34} }
 @inproceedings{nikoukhah_campbell_delebecque_1999, title={Detection Signal Design for Failure Detection}, booktitle={Proceedings of the Iranian Conference on Electrical Engineering}, author={Nikoukhah, R. and Campbell, S.L. and Delebecque, F.}, year={1999}, pages={45–52} }
 @book{betts_huffman_biehn_campbell_1999, title={Exploiting order variation in mesh refinement for direct transcription methods}, institution={Boeing}, author={Betts, John T. and Huffman, William P. and Biehn, Neil and Campbell, Stephen L.}, year={1999} }
 @article{nikoukhah_campbell_delebecque_1999, title={Kalman filtering for general discrete-time linear systems}, volume={44}, ISSN={["0018-9286"]}, DOI={10.1109/9.793722}, abstractNote={Recursive state estimation problems for explicit and implicit time-invariant linear systems, both for systems with and without unknown inputs, can be formulated as a single problem usually referred to as descriptor Kalman filtering. Solutions to this problem have been proposed in the literature; however, these solutions either neglect possible contributions of future dynamics to the current estimate or make unnecessary assumptions on the structure of the system. In this paper, the authors propose a solution to this problem which leads to a constructive method lifting these unnecessary assumptions. This method uses a generalization of the shuffle algorithm.}, number={10}, journal={IEEE TRANSACTIONS ON AUTOMATIC CONTROL}, author={Nikoukhah, R and Campbell, SL and Delebecque, F}, year={1999}, month={Oct}, pages={1829–1839} }
 @inproceedings{betts_huffman_biehn_campbell_1999, title={Mesh refinement that exploits order variation}, booktitle={Proceedings of the Workshop: Optimalsteuerungsprobleme in der Luft- und Raumfahrt, Universitat Greifswald, 7/8 Oktober 1999  (Sonderforschungsbereich; 255)}, publisher={Munchen: Hieronymus}, author={Betts, J. T. and Huffman, W. P. and Biehn, N. and Campbell, S.L.}, year={1999}, pages={1–12} }
 @inbook{campbell_nikoukhah_delebecque_1999, title={Nonlinear descriptor systems}, DOI={10.1007/978-1-4471-0853-5_9}, booktitle={Advances in control: Highlights of ECC '99}, publisher={London; New York: Springer-Verlag}, author={Campbell, Stephen and Nikoukhah, R. and DeLebecque, F.}, year={1999}, pages={247–282} }
 @article{campbell_marszalek_1999, title={The index of an infinite dimensional implicit system}, volume={5}, ISSN={["1387-3954"]}, DOI={10.1076/mcmd.5.1.18.3625}, abstractNote={The idea of the index of a differential algebraic equation (DAE) (or implicit differential equation) has played a fundamental role in both the analysis of DAEs and the development of numerical algorithms for DAEs. DAEs frequently arise as partial discretizations of partial differential equations (PDEs). In order to relate properties of the PDE to those of the resulting DAE it is necessary to have a concept of the index of a possibly constrained PDE. Using the finite dimensional theory as motivation, this paper will examine what one appropriate analogue is for infinite dimensional systems. A general definition approach will be given motivated by the desire to consider numerical methods. Specific examples illustrating several kinds of behavior will be considered in some detail. It is seen that our definition differs from purely algebraic definitions. Numerical solutions, and simulation difficulties, can be misinterpreted if this index information is missing.}, number={1}, journal={MATHEMATICAL AND COMPUTER MODELLING OF DYNAMICAL SYSTEMS}, author={Campbell, SL and Marszalek, W}, year={1999}, month={Mar}, pages={18–42} }
 @inbook{campbell_marszalek_1998, title={The interaction between simulation and modeling in infinite dimensional systems}, DOI={10.1142/9789814447317_0053}, abstractNote={Theory and Practice of Control and Systems, pp. 322-327 (1999) No AccessTHE INTERACTION BETWEEN SIMULATION AND MODELING IN INFINITE DIMENSIONAL SYSTEMSS. L. CAMPBELL and W. MARSZALEKS. L. CAMPBELLDepartment of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA and W. MARSZALEKShawnee State University, Portsmouth, Ohio, 45662, USAhttps://doi.org/10.1142/9789814447317_0053Cited by:0 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: In many applications involving PDE models it is standard engineering practice to replace the PDEs by a finite dimensional system of ordinary differential equations. Sometimes this approximation forms a differential algebraic equations (DAE). Recently it has been recognized in several areas that the choice of approximation needs to take into account the numerical and analytic properties of the finite dimensional DAE approximation. In this paper we examine how to recognise when simulation difficulties are due to the approximation or modeling as opposed to being intrinsic difficults of the problem being considered. Intuition and illustrative examples are stressed as opposed to detailed theoretical results. FiguresReferencesRelatedDetails Theory and Practice of Control and SystemsMetrics History PDF download}, booktitle={Theory and practice of control: proceedings of the 6th IEEE Mediterranean Conference, Alghero, Sardinia, Italy 9-11 June 1998}, publisher={Singapore; River Edge, NJ: World Scientific}, author={Campbell, Stephen and Marszalek, W.}, editor={A. Tornambae, G. Conte and Perdon, A. M.Editors}, year={1998}, pages={322–327} }
 @article{campbell_yeomans_1998, title={Behavior of the nonunique terms in general DAE integrators}, volume={28}, ISSN={["0168-9274"]}, DOI={10.1016/S0168-9274(98)00044-0}, abstractNote={Differential algebraic equations (DAEs) are implicit systems of ordinary differential equations F(y′, y, t) = 0. DAEs arise in many applications and a variety of numerical methods have been developed for solving DAEs. Numerical methods have been proposed for integrating general higher index DAEs and successfully applied to test problems. These methods require solving a nonlinear system of equations which is larger than the original DAE at each time step. For fully implicit problems part of the solution of the nonlinear system is not uniquely determined. This poses questions about the effects of predictors and also a possible instability in the growth of these terms during a numerical integration. In this paper it is shown that the nonunique component is actually the numerical solution of an auxiliary DAE which depends not only on the original DAE but also on the predictor being used in the Gauss-Newton iteration. As an important consequence we both establish a basis for the design of low order integrators for high index DAEs and develop guidelines for the use of predictors in integrating general high index DAEs.}, number={2-4}, journal={APPLIED NUMERICAL MATHEMATICS}, author={Campbell, SL and Yeomans, KD}, year={1998}, month={Oct}, pages={209–226} }
 @article{campbell_hollenbeck_yeomans_zhong_1998, title={Mixed symbolic-numerical computations with general DAEs I: System properties}, volume={19}, ISSN={["1017-1398"]}, DOI={10.1023/A:1019154423096}, number={1-4}, journal={Numerical Algorithms}, author={Campbell, Stephen L. and Hollenbeck, R. and Yeomans, K. and Zhong, Y.}, year={1998}, pages={73–83} }
 @article{campbell_marszalek_1998, title={Mixed symbolic-numerical computations with general DAEs II: An applications case study}, volume={19}, ISSN={["1017-1398"]}, DOI={10.1023/A:1019106507166}, number={1-4}, journal={Numerical Algorithms}, author={Campbell, Stephen L. and Marszalek, W.}, year={1998}, pages={85–94} }
 @article{nikoukhah_campbell_delebecque_1998, title={Observer design for general linear time-invariant systems}, volume={34}, ISSN={["0005-1098"]}, DOI={10.1016/S0005-1098(98)00003-X}, abstractNote={It is noted that, for both explicit and implicit linear systems, several observer design problems, including system inversion, for systems with or without unknown inputs can all be formulated as a single problem involving descriptor systems. The method used for solving this problem is based on recursively applying the reduction operation which consists of identifying and discarding equations that do not provide useful information for the estimation problem. The reduction algorithm produces a reduced dimension system for which standard observers can be constructed. The method presented can be implemented using numerically robust algorithms. One such algorithm is presented.}, number={5}, journal={AUTOMATICA}, author={Nikoukhah, R and Campbell, SL and Delebecque, F}, year={1998}, month={May}, pages={575–583} }
 @article{campbell_marszalek_1997, title={DAEs arising from traveling wave solutions of PDEs}, volume={82}, ISSN={["0377-0427"]}, DOI={10.1016/S0377-0427(97)00084-8}, abstractNote={The study of traveling waves for explicit and implicit PDEs can sometimes result in differential algebraic equations (DAEs) instead of ordinary differential equations. The advantages of using DAEs is discussed as are the implications of DAE theory for the study of traveling waves. A specific type of traveling wave that connects equilibria is examined in more detail. Specific examples are given.}, number={1-2}, journal={JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS}, author={Campbell, SL and Marszalek, W}, year={1997}, month={Sep}, pages={41–58} }
 @article{campbell_zhong_1997, title={Jacobian reuse in explicit integrators for higher index DAEs}, volume={25}, ISSN={["0168-9274"]}, DOI={10.1016/S0168-9274(97)00052-4}, abstractNote={Systems F(y′,y,t) = 0 with Fy′ identically singular are known as differential algebraic equations (DAEs) and occur in a variety of applications. The index v is one measure of numerical difficulty. Most numerical methods for DAEs either require special structure or low index. Two alternative approaches have been proposed for numerically integrating more general higher index DAEs. This paper examines some of the mathematical issues involved in the efficient implementation of the “explicit integration” method. It is first shown that the reuse of Jacobians can lead to the integration of discontinuous vector fields. It is then proven that these discontinuous fields can be successfully integrated. Computational examples back up the theory. A comparison to a standard integrator on an index three control problem illustrates that while the explicit approach can be somewhat more expensive computationally, it can be easier to apply, and does not suffer from order reduction in the higher index variables.}, number={4}, journal={APPLIED NUMERICAL MATHEMATICS}, author={Campbell, SL and Zhong, YC}, year={1997}, month={Dec}, pages={391–412} }
 @inproceedings{campbell_hollenbeck_marszalek_1997, title={Mixed symbolic-numerical computations with general DAEs}, booktitle={Proceedings of the Symposium on Differential-Algebraic Equations: Algebraic and Numerical Aspects}, author={Campbell, Stephen L. and Hollenbeck, R. and Marszalek, W.}, year={1997}, pages={23–34} }
 @article{campbell_delebecque_nikoukhah_1997, title={Observer design for linear time varying descriptor systems}, volume={1}, journal={Proceedings of the Control Industrial Systems}, author={Campbell, Stephen L. and Delebecque, F. and Nikoukhah, R.}, year={1997}, pages={507–512} }
 @article{vonwissel_nikoukhah_campbell_delebecque_1997, title={The effects of computational delay in descriptor-based trajectory tracking control}, volume={67}, ISSN={["1366-5820"]}, DOI={10.1080/002071797224289}, abstractNote={Descriptor Predictive Control (DPC) has been shown to be a useful method for solving nonlinear tracking problems. A rigorous analysis of local stability and performance characteristics of this method has been achieved previously by studying the linear plant under the assumption that the delay introduced in the control due to numerical computation can be neglected. It was shown that, if the plant is controllable and minimum phase, stability is guaranteed and tracking is achieved exponentially with any desired rate of convergence. It was also shown that sometimes DPC must include a specially designed preliminary feedback. In this paper, we carry out a similar analysis by taking into account computational delay, which is unavoidable in actual implementation of DPC. We show, in particular, that under the same assumptions, and provided the special preliminary feedback is used, that the closed loop system remains stable as long as the delay is smaller than a threshold and that exponential tracking is achieved. ...}, number={2}, journal={INTERNATIONAL JOURNAL OF CONTROL}, author={vonWissel, D and Nikoukhah, R and Campbell, SL and Delebecque, F}, year={1997}, month={May}, pages={251–273} }
 @inbook{campbell_hollenbeck_1996, title={Automatic differentiation and implicit differential equations}, booktitle={Computational differentiation: Techniques, applications, and tools}, publisher={Philadelphia: SIAM}, author={Campbell, S. L. and Hollenbeck, R.}, editor={B. Berz, C. Bischof and G. Corliss and Griewank, A.Editors}, year={1996} }
 @inproceedings{campbell_kelley_yeomans_1996, place={Lille, France}, title={Consistent initial conditions for unstructured higher index DAEs: A computational study}, booktitle={Proceedings of Computational Engineering in Systems Applications}, author={Campbell, Stephen L. and Kelley, C.T. and Yeomans, K.D.}, year={1996}, pages={416–421} }
 @article{campbell_moore_zhong_1996, title={Constraint Preserving Integrators for Unstructured Higher Index DAEs}, journal={Zeitschrift fuer Angewandte Mathematik und Mechanik (ZAMM)}, author={Campbell, Stephen L. and Moore, E. and Zhong, Y.}, year={1996}, pages={83–86} }
 @article{campbell_ipsen_kelley_meyer_xue_1996, title={Convergence Estimates for Solution of Integral Equations with GMRES}, volume={8}, ISSN={0897-3962}, url={http://dx.doi.org/10.1216/jiea/1181075914}, DOI={10.1216/jiea/1181075914}, abstractNote={In this paper we derive convergence estimates for the iterative solution of nonsymmetric linear systems by GMRES. We work in the context of strongly convergent-collectively compact sequences of approximations to linear compact xed point problems. Our estimates are intended to explain the observations that the performance of GMRES is independent of the discretization if the resolution of the discretization is su ciently good. Our bounds are independent of the right hand side of the equation, re ect the r-superlinear convergence of GMRES in the in nite dimensional setting, and also allow for more than one implementation of the discrete scalar product. Our results are motivated by quadrature rule approximation to second-kind Fredholm integral equations.}, number={1}, journal={Journal of Integral Equations and Applications}, publisher={Rocky Mountain Mathematics Consortium}, author={Campbell, S.L. and Ipsen, I.C.F. and Kelley, C.T. and Meyer, C.D. and Xue, Z.Q.}, year={1996}, month={Mar}, pages={19–34} }
 @inproceedings{campbell_von wissel_nikoukhah_delebecque_1996, place={Lille, France}, title={Descriptor predictive control: tracking controllers for a riderless bicycle}, booktitle={Proceedings of Computational Engineering in Systems Applications}, author={Campbell, Stephen L. and von Wissel, D. and Nikoukhah, R. and Delebecque, F.}, year={1996}, pages={292–297} }
 @article{campbell_ipsen_kelley_meyer_1996, title={GMRES and the minimal polynomial}, volume={36}, ISSN={0006-3835 1572-9125}, url={http://dx.doi.org/10.1007/bf01733786}, DOI={10.1007/BF01733786}, abstractNote={We present a qualitative model for the convergence behaviour of the Generalised Minimal Residual (GMRES) method for solving nonsingular systems of linear equationsAx =b in finite and infinite dimensional spaces. One application of our methods is the solution of discretised infinite dimensional problems, such as integral equations, where the constants in the asymptotic bounds are independent of the mesh size. Our model provides simple, general bounds that explain the convergence of GMRES as follows: If the eigenvalues ofA consist of a single cluster plus outliers then the convergence factor is bounded by the cluster radius, while the asymptotic error constant reflects the non-normality ofA and the distance of the outliers from the cluster. If the eigenvalues ofA consist of several close clusters, then GMRES treats the clusters as a single big cluster, and the convergence factor is the radius of this big cluster. We exhibit matrices for which these bounds are tight. Our bounds also lead to a simpler proof of existing r-superlinear convergence results in Hilbert space.}, number={4}, journal={BIT Numerical Mathematics}, publisher={Springer Science and Business Media LLC}, author={Campbell, Stephen L. and Ipsen, I.C.F. and Kelley, C.T. and Meyer, C.D.}, year={1996}, pages={664–675} }
 @inproceedings{campbell_von wissel_nikoukhah_delebecque_1996, place={Lille, France}, title={Nonlinear observer design using implicit system descriptions}, booktitle={Proceedings of Computational Engineering in Systems Applications}, author={Campbell, Stephen L. and von Wissel, D. and Nikoukhah, R. and Delebecque, F.}, editor={Wissel, Stephen L.Campbell and Nikoukhah, R. and Delebecque, F.Editors}, year={1996}, pages={404–409} }
 @article{campbell_marszalek_1996, title={ODE/DAE Integrators and MOL Problems}, journal={Zeitschrift fuer Angewandte Mathematik und Mechanik (ZAMM)}, author={Campbell, Stephen L. and Marszalek, W.}, year={1996}, pages={251–254} }
 @inproceedings{campbell_delebecque_nikoukhah_1996, place={New York}, title={Pencil algorithms and observer design}, ISBN={9780780330320 9780780330337}, booktitle={Proceedings of the 1996 IEEE International Symposium on Computer-Aided Control System Design (CACSD)}, publisher={Institute of Electrical and Electronics Engineers}, author={Campbell, Stephen L. and Delebecque, F. and Nikoukhah, R.}, year={1996}, pages={83–88} }
 @article{campbell_moore_1995, title={Constraint preserving integrators for general nonlinear higher index DAEs}, volume={69}, ISSN={0029-599X 0945-3245}, url={http://dx.doi.org/10.1007/s002110050099}, DOI={10.1007/s002110050099}, number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Campbell, Stephen L. and Moore, Edward}, year={1995}, month={Feb}, pages={383–399} }
 @article{campbell_1995, title={High-Index Differential Algebraic Equations}, volume={23}, ISSN={0890-5452}, url={http://dx.doi.org/10.1080/08905459508905235}, DOI={10.1080/08905459508905235}, abstractNote={ABSTRACT In the last few years there has been considerable research on differential algebraic equations (DAEs) f(x1, x, t) = 0, where fx 1 is identically singular. The index provides one measure of the singularity of a DAE. Most of the numerical analysis literature on DAEs to date has dealt with DAEs with indices no larger than three, because of technical difficulties and because many basic applications including constrained mechanical systems have this index. This paper discusses several situations where DAEs of index higher than three occur naturally. It will also discuss the relationship between certain concepts in nonlinear control theory such as relative degree and zero dynamics, the index, and constrained mechanical systems.}, number={2}, journal={Mechanics of Structures and Machines}, publisher={Informa UK Limited}, author={Campbell, Stephen L}, year={1995}, month={Jan}, pages={199–222} }
 @article{campbell_1995, title={Linearization of DAEs along trajectories}, volume={46}, ISSN={0044-2275 1420-9039}, url={http://dx.doi.org/10.1007/bf00952257}, DOI={10.1007/bf00952257}, number={1}, journal={ZAMP Zeitschrift f�r angewandte Mathematik und Physik}, publisher={Springer Science and Business Media LLC}, author={Campbell, Stephen L.}, year={1995}, month={Jan}, pages={70–84} }
 @inproceedings{campbell_zhu_lewis_ito_1995, title={Maneuver planning and robust path tracking for mobile robotic nonholonomic systems}, booktitle={Proceedings of the European Control Conference}, author={Campbell, Stephen L. and Zhu, S.Q. and Lewis, F.L. and Ito, K.}, year={1995}, pages={3080–3085} }
 @article{campbell_1995, title={Nonregular 2D descriptor delay systems}, volume={12}, ISSN={0265-0754 1471-6887}, url={http://dx.doi.org/10.1093/imamci/12.1.57}, DOI={10.1093/imamci/12.1.57}, abstractNote={This paper examines descriptor systems with delays which are in the form Bx′(t) + Dx(t) + Cx(t − α) = Eu(t) . Previous paper have examined the case when λB + D is a regular pencil. In this paper we examine the case when λ B + D is a singular pencil but det(λ B + D + ω C )≢0. Behaviour not previously reported for descriptor systems is observed. Several basic issues are discussed.}, number={1}, journal={IMA Journal of Mathematical Control and Information}, publisher={Oxford University Press (OUP)}, author={Campbell, Stephen L.}, year={1995}, pages={57–67} }
 @article{campbell_von wissel_nikoukhah_delebecque_1995, title={Numerically Generated Path Stabilizing Controllers: Use of Preliminary Feedback}, volume={31}, number={6}, journal={Kybernetika}, author={Campbell, Stephen L. and von Wissel, Dirk and Nikoukhah, Ramine and Delebecque, Francois}, year={1995}, pages={657–668} }
 @article{campbell_griepentrog_1995, title={Solvability of General Differential Algebraic Equations}, volume={16}, ISSN={1064-8275 1095-7197}, url={http://dx.doi.org/10.1137/0916017}, DOI={10.1137/0916017}, abstractNote={In the last few years there has been considerable research on differential algebraic equations (DAEs) $f(t,x,x') = 0$ where $f_{x'} $ is identically singular. Most of this effort has focused on computing a solution that is assumed to exist. That is, the DAE is assumed solvable. More recently there have been existence results developed using differential geometry. For complex higher index systems these characterizations can be hard to verify in practice. In this paper the computational verification of solvability is investigated. This first requires developing an alternative set of sufficient conditions for solvability which are more amenable to computation. Verification of these conditions using readily available numerical and symbolic software is then discussed. An example from robotics where classical graph theoretical approaches give an incorrect answer is worked to illustrate the usefulness of the sufficient condition and the computational approach.}, number={2}, journal={SIAM Journal on Scientific Computing}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Campbell, Stephen L. and Griepentrog, E.}, year={1995}, month={Mar}, pages={257–270} }
 @inproceedings{campbell_delebecque_nikoukhah_von wissel_1995, title={The geometry of square invertible linear systems, matrix pencils, and predictive control}, booktitle={Proceedings of the third European Control Conference (ECC 95)}, author={Campbell, Stephen L. and Delebecque, F. and Nikoukhah, R. and von Wissel, D.}, editor={Isidori, A. and Bittanti, S. and Mosca, E. and De Luca, A. and Di Benedetto, M.D. and Oriolo, G.Editors}, year={1995}, pages={2962–2967} }
 @article{campbell_gear_1995, title={The index of general nonlinear DAEs}, volume={72}, ISSN={0029-599X 0945-3245}, url={http://dx.doi.org/10.1007/s002110050165}, DOI={10.1007/s002110050165}, number={2}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Campbell, Stephen L. and Gear, C. William}, year={1995}, month={Dec}, pages={173–196} }
 @inproceedings{campbell_moore_1994, title={A Coordinate Free Approach for Constraint Preserving Higher Index DAE Integrators}, booktitle={Proc. 94 IMACS World Congress on Scientific Computation}, author={Campbell, Stephen L. and Moore, E.}, year={1994}, pages={65–68} }
 @inproceedings{campbell_zhong_1994, place={Atlanta, Georgia}, title={Computational speedup for general nonlinear higher index DAE integrators}, booktitle={IMACS '94 : proceedings of the 14th IMACS World congress on computation and applied mathematics}, publisher={Georgia Institute of Technology}, author={Campbell, Stephen L. and Zhong, Y.}, year={1994}, pages={69–73} }
 @inproceedings{campbell_1994, title={DAE Approximations of PDE Modeled Control Problems}, booktitle={Proceedings of the 2nd IEEE Mediterranean Symposium on New Directions in Control and Automation}, author={Campbell, Stephen L.}, year={1994}, pages={407–414} }
 @article{campbell_rakowski_1994, title={Explicit formulae for completions of linear time varying singular systems of differential equations}, volume={13}, ISSN={0278-081X 1531-5878}, url={http://dx.doi.org/10.1007/bf01188105}, DOI={10.1007/bf01188105}, number={2-3}, journal={Circuits, Systems, and Signal Processing}, publisher={Springer Science and Business Media LLC}, author={Campbell, Stephen L. and Rakowski, Marek}, year={1994}, month={Jun}, pages={185–199} }
 @article{campbell_1994, title={Numerical Methods for Unstructured Higher Index DAEs}, volume={1}, journal={Annals of Numerical Mathematics}, author={Campbell, Stephen L.}, year={1994}, pages={265–278} }
 @article{campbell_moore_1994, title={Progress on a general numerical method for nonlinear higher index DAEs II}, volume={13}, ISSN={0278-081X 1531-5878}, url={http://dx.doi.org/10.1007/bf01188101}, DOI={10.1007/bf01188101}, number={2-3}, journal={Circuits, Systems, and Signal Processing}, publisher={Springer Science and Business Media LLC}, author={Campbell, Stephen L. and Moore, Edward}, year={1994}, month={Jun}, pages={123–138} }
 @article{campbell_moore_zhong_1994, title={Utilization of automatic differentiation in control algorithms}, volume={39}, ISSN={0018-9286}, url={http://dx.doi.org/10.1109/9.284891}, DOI={10.1109/9.284891}, abstractNote={Symbolic languages are increasingly being used in the analysis and implementation of control algorithms. Many of these control procedures involve some type of differentiation or Jacobian formulation. Automatic differentiation provides an alternative means of computing this information which is rarely considered in the control literature. This correspondence discusses the use of automatic differentiation. Numerical results comparing the use of automatic differentiation and symbolic approaches in the context of a particular nonlinear control system are given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>}, number={5}, journal={IEEE Transactions on Automatic Control}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Campbell, S.L. and Moore, E. and Zhong, Yangchun}, year={1994}, month={May}, pages={1047–1052} }
 @article{campbell_1993, title={Least squares completions for nonlinear differential algebraic equations}, volume={65}, ISSN={0029-599X 0945-3245}, url={http://dx.doi.org/10.1007/bf01385741}, DOI={10.1007/bf01385741}, number={1}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Campbell, Stephen L.}, year={1993}, month={Dec}, pages={77–94} }
 @inproceedings{campbell_1992, place={Dallas}, title={A survey of time varying and nonlinear descriptor control systems}, booktitle={Proceedings 1992 International Symposium on Implicit & Nonlinear Systems, Automation and Robotics}, author={Campbell, Stephen L.}, year={1992}, pages={356–363} }
 @article{campbell_1992, title={Uniqueness of completions for linear time varying differential algebraic equations}, volume={161}, ISSN={0024-3795}, url={http://dx.doi.org/10.1016/0024-3795(92)90005-u}, DOI={10.1016/0024-3795(92)90005-u}, abstractNote={The extent to which a completion x′=G(t)x+∑ri=0Ri(t)f(i)(t) of a linear ti me varying differential algebraic equation E(t)x′(t)+F(t)x(t)=f(t) is unique is carefully examined. The implications for numerical methods for solving DAEs based on differentiated equations are discussed.}, journal={Linear Algebra and its Applications}, publisher={Elsevier BV}, author={Campbell, Stephen L.}, year={1992}, month={Jan}, pages={55–67} }
 @inproceedings{campbell_1991, place={Dublin}, title={2-D (differential-delay) implicit systems}, booktitle={IMACS '91 : proceedings of the 13th IMACS World Congress on Computation and Applied Mathematics : July 22-26, 1991, Trinity College, Dublin, Ireland}, publisher={Criterion Press}, author={Campbell, Stephen L.}, year={1991}, pages={1828–1829} }
 @article{campbell_1991, title={Comments on 2-D descriptor systems}, volume={27}, ISSN={0005-1098}, url={http://dx.doi.org/10.1016/0005-1098(91)90020-3}, DOI={10.1016/0005-1098(91)90020-3}, abstractNote={This paper discusses general 2-D descriptor systems of the form Exi+1,j+1 = Axi,j + Bxi+1,j + Cxi,j+1 + D0ui,j + D1ui+1,j + D2ui,j+1. Solution formula and structural forms are developed for several large classes of 2-D descriptor systems. The idea of a recursive chain is introduced. It is shown that these systems include several types of behavior not discussed elsewhere in the literature.}, number={1}, journal={Automatica}, publisher={Elsevier BV}, author={Campbell, Stephen L.}, year={1991}, month={Jan}, pages={189–192} }
 @article{campbell_leimkuhler_1991, title={Differentiation of Constraints in Differential-Algebraic Equations∗}, volume={19}, ISSN={0890-5452}, url={http://dx.doi.org/10.1080/08905459108905136}, DOI={10.1080/08905459108905136}, abstractNote={ABSTRACT ABSTRACT Differentiation of constraints that appear in differential-algebraic equations (DAEs) has been advocated for many purposes, ranging from index reduction for numerical purposes to systems inversion in control theory. In this paper, the numerical and analytic consequences of such differentiations are studied and criteria are established for when difficulties can occur.}, number={1}, journal={Mechanics of Structures and Machines}, publisher={Informa UK Limited}, author={Campbell, Stephen L. and Leimkuhler, B.}, year={1991}, month={Jan}, pages={19–39} }
 @article{campbell_nichols_terrell_1991, title={Duality, observability, and controllability for linear time-varying descriptor systems}, volume={10}, ISSN={0278-081X 1531-5878}, url={http://dx.doi.org/10.1007/bf01194883}, DOI={10.1007/bf01194883}, number={4}, journal={Circuits Systems and Signal Processing}, publisher={Springer Science and Business Media LLC}, author={Campbell, Stephen L. and Nichols, Nancy K. and Terrell, William J.}, year={1991}, month={Dec}, pages={455–470} }
 @inproceedings{campbell_1991, place={Dublin}, title={Least squares completions for nonlinear index three Hessenberg DAEs}, booktitle={IMACS '91 : proceedings of the 13th IMACS World Congress on Computation and Applied Mathematics : July 22-26, 1991, Trinity College, Dublin, Ireland}, publisher={Criterion}, author={Campbell, Stephen L.}, year={1991}, pages={1145–1148} }
 @article{campbell_terrell_1991, title={Observability of Linear Time-Varying Descriptor Systems}, volume={12}, ISSN={0895-4798 1095-7162}, url={http://dx.doi.org/10.1137/0612035}, DOI={10.1137/0612035}, abstractNote={A characterization of observability for linear time-varying descriptor systems $E( t )x' ( t ) + F ( t ) x ( t ) = B (t) u (t), y ( t ) = C ( t ) x ( t )$, is given. E is not required to have constant rank. The characterization is designed to reduce symbolic computation and has potential advantages even when E is nonsingular. It is also shown that all observable analytic descriptor systems are smoothly observable even if they are not uniformly observable. Finally, the external behavior of time-varying descriptor systems is characterized.}, number={3}, journal={SIAM Journal on Matrix Analysis and Applications}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Campbell, Stephen L. and Terrell, William J.}, year={1991}, month={Jul}, pages={484–496} }
 @article{campbell_clark_1990, title={Convergence of BDF approximations for nonsolvable differential algebraic equations}, volume={6}, ISSN={0168-9274}, url={http://dx.doi.org/10.1016/0168-9274(90)90009-5}, DOI={10.1016/0168-9274(90)90009-5}, abstractNote={Abstract It is shown that a BDF method applied to a differential algebraic equation, F ( t , z , z ') = 0, can have a unique limit as the stepsize goes to zero even if the differential algebraic equation does not have unique solutions.}, number={3}, journal={Applied Numerical Mathematics}, publisher={Elsevier BV}, author={Campbell, Stephen L. and Clark, Kenneth D.}, year={1990}, month={Mar}, pages={153–158} }
 @inproceedings{campbell_1990, title={Descriptor systems in the 1990s}, url={http://dx.doi.org/10.1109/cdc.1990.203638}, DOI={10.1109/cdc.1990.203638}, abstractNote={After briefly summarizing the growth in the theory of descriptors, or differential algebraic equations (DAEs), over the last two decades, the current challenges and potential successes are discussed. Among these major challenges facing DAE theory are: numerical software for index 3 systems; implicit Runge-Kutta code for low index problems; boundary value problem numerical codes; linearization; new numerical techniques; the initialization problem; direct control information computing; parameter identification; noisy systems; utilization of constraints; implementation for time invariant control; extra derivatives; large-scale DAEs; real-time simulation: and new types of systems.<<ETX>>}, booktitle={29th IEEE Conference on Decision and Control}, publisher={IEEE}, author={Campbell, S.L.}, year={1990} }
 @article{campbell_yeomans_1990, title={Solving Singular Systems Using Orthogonal Functions}, volume={137}, ISSN={0143-7054}, url={http://dx.doi.org/10.1049/ip-d.1990.0027}, DOI={10.1049/ip-d.1990.0027}, abstractNote={Orthogonal functions, and, in particular, Walsh functions, have been advocated in the literature as a method of approximating the solutions of singular systems Ex'=Fx+Bu of index k. The paper gives the first analysis of the accuracy of these approximations. For Walsh functions, divergence is shown for k>or=3 and convergence for k=0,1. The k=2 case is also analysed. >}, number={4}, journal={IEE Proceedings D Control Theory and Applications}, publisher={Institution of Engineering and Technology (IET)}, author={Campbell, S.L. and Yeomans, K.D.}, year={1990}, pages={222} }
 @article{campbell_1989, title={A computational method for general higher index nonlinear singular systems of differential equations}, volume={1}, number={2}, journal={IMACS Transactions on Scientific Computing}, author={Campbell, Stephen L.}, year={1989}, pages={555–560} }
 @article{campbell_1989, title={Comments on functional reproducibility of time-varying input-output systems}, volume={34}, ISSN={0018-9286 1558-2523}, url={http://dx.doi.org/10.1109/9.29447}, DOI={10.1109/9.29447}, abstractNote={Recent results on solvability developed as part of a conjecture of K.A. Grasse (SIAM J. Contr. Optimiz., vol.26, p.230-249, 1988) on the necessity of certain rank conditions is answered for an important class of systems. A simpler description of the derivative arrays is presented. An alternative way of computing the control producing a given output is presented. >}, number={8}, journal={IEEE Transactions on Automatic Control}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Campbell, S.L.}, year={1989}, month={Aug}, pages={922–924} }
 @article{campbell_1989, title={Distributional convergence of BDF approximations to solutions of descriptor systems}, volume={8}, ISSN={0278-081X 1531-5878}, url={http://dx.doi.org/10.1007/bf01598414}, DOI={10.1007/bf01598414}, number={3}, journal={Circuits, Systems, and Signal Processing}, publisher={Springer Science and Business Media LLC}, author={Campbell, Stephen L.}, year={1989}, month={Sep}, pages={261–265} }
 @inproceedings{campbell_1989, title={The Numerical Solution of Singular Systems Arising in Control Problems}, url={http://dx.doi.org/10.23919/acc.1989.4790540}, DOI={10.23919/acc.1989.4790540}, abstractNote={This paper surveys numerical methods for the solution of singular systems that arise in control theory. Methods limited to linear time invariant systems will not be discussed.}, booktitle={1989 American Control Conference}, publisher={IEEE}, author={Campbell, Stephen L.}, year={1989}, month={Jun} }
 @inbook{campbell_1988, place={Philadelphia, PA}, title={Bilinear nonlinear descriptor control systems in Linear Algebra in Signals, Systems, and Control}, booktitle={Linear algebra in signals, systems, and control : proceedings of the Conference on Linear Algebra in Signals, Systems, and Control, Boston, Massachusetts, August 12-14, 1986}, publisher={Society for Industrial and Applied Mathematics}, author={Campbell, Stephen L.}, editor={Datta, B.N.Editor}, year={1988}, pages={439–511} }
 @article{campbell_1988, title={Control problem structure and the numerical solution of linear singular systems}, volume={1}, ISSN={0932-4194 1435-568X}, url={http://dx.doi.org/10.1007/bf02551237}, DOI={10.1007/bf02551237}, number={1}, journal={Mathematics of Control, Signals, and Systems}, publisher={Springer Science and Business Media LLC}, author={Campbell, Stephen L.}, year={1988}, month={Feb}, pages={73–87} }
 @inbook{campbell_clark_1988, place={North Holland}, title={Singular control problem structure and the convergence of backward differentiation formulas}, booktitle={Linear Circuits, Systems, and Signal Processing}, author={Campbell, Stephen L. and Clark, K.D.}, editor={Brynes, C.I. and Martin, C.F. and Saeks, R.E.Editors}, year={1988}, pages={19–26} }
 @article{campbell_1987, title={A General Form for Solvable Linear Time Varying Singular Systems of Differential Equations}, volume={18}, ISSN={0036-1410 1095-7154}, url={http://dx.doi.org/10.1137/0518081}, DOI={10.1137/0518081}, abstractNote={A canonical form is derived for all linear solvable systems $E(t)x'(t) + F(t)x(t) = f(t)$ with sufficiently smooth coefficients E, F Using this form it is shown that for all smooth enough solvable ...}, number={4}, journal={SIAM Journal on Mathematical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Campbell, Stephen L.}, year={1987}, month={Jul}, pages={1101–1115} }
 @article{campbell_1987, title={Comment on controlling generalized state-space (descriptor) systems}, volume={46}, ISSN={0020-7179 1366-5820}, url={http://dx.doi.org/10.1080/00207178708934045}, DOI={10.1080/00207178708934045}, abstractNote={some confusion in the literature on the controllability of descriptor systems is cleared up.}, number={6}, journal={International Journal of Control}, publisher={Informa UK Limited}, author={Campbell, Stephen L.}, year={1987}, month={Dec}, pages={2229–2230} }
 @book{campbell_terrell_1987, title={Derivative Arrays, Geometric Control Theory, and Realizations of Linear Descriptor Systems.}, url={http://dx.doi.org/10.21236/ada190882}, DOI={10.21236/ada190882}, abstractNote={Abstract : The relationship between numerical methods for realizations of E(t)x'(t) + F(t)x(t)=f(t) based on derivative arrays and geometric control realization procedures based on Lie derivatives is examined.}, institution={Defense Technical Information Center}, author={Campbell, Stephen L. and Terrell, William J.}, year={1987}, month={Nov} }
 @article{distributional convergence of bdf (backward differentiation formulas) approximations to solutions of descriptor systems._1987, DOI={10.21236/ada190819}, abstractNote={Abstract : It has been frequently observed that the backward differentiation approximation of the solutions of Ex' + Fx = f can fail to converge even pointwise in an initial boundary layer. This note shows that the approximations converge in a distributional sense even if the exact solution is also distributional. Keywords: Matrices; Convergence; Approximation.}, journal={Defense Technical Information Center}, year={1987} }
 @inproceedings{campbell_1987, title={Local realizations of time varying descriptor systems}, url={http://dx.doi.org/10.1109/cdc.1987.272582}, DOI={10.1109/cdc.1987.272582}, abstractNote={A method of realizing a descriptor system E(t)x'(t)+F(t)x(t) = B(t)u(t) as a state space system y' = A(t)y(t) + ¿i=0 lKi(t)u(i)(t) x = M(t)y(t) + ¿i=0 lNi(t)u(i)(t) is developed. This realization has the important property that the coefficients A, Ki, M, N, are computed directly from arrays of derivatives of E, F, B, u. Thus no time varying coordinate changes need to be performed prior to any differentiations making the method easy to implement numerically.}, booktitle={26th IEEE Conference on Decision and Control}, publisher={IEEE}, author={Campbell, Stephen L.}, year={1987}, month={Dec} }
 @inbook{campbell_1987, place={New York}, title={Operator methods and singular control problems}, ISBN={9780824778118}, booktitle={Operator Methods for Optimal Control Problems}, publisher={Marcel Dekker}, author={Campbell, Stephen L.}, editor={Lee, Sung JEditor}, year={1987}, pages={57–66} }
 @book{campbell_yeomans_1987, title={Solving Singular Systems Using Orthogonal Functions.}, DOI={10.21236/ada190881}, journal={Defense Technical Information Center}, institution={Defense Technical Information Center}, author={Campbell, Stephen L. and Yeomans, Kevin D.}, year={1987}, month={Oct} }
 @article{the numerical and analytic analysis of implicit differential equations and their application to control and circuit problems._1987, DOI={10.21236/ada185531}, abstractNote={Abstract : Results on the numerical and analytic solution of implicit systems of differential equations and their application to circuit and control problems were developed. In particular, the first general algorithm for the linear time varying case was developed along with an analysis of how to apply it to certain control problems. New structure theorems provide insight on the convergence of backward differentiation formulas and guidelines for their use. (Author)}, journal={Defense Technical Information Center}, year={1987} }
 @inbook{campbell_1986, place={Amsterdam}, title={Consistent initial conditions for linear time varying singular systems}, ISBN={9780444700384}, booktitle={Frequency Domain and State Space Methods for Linear Systems}, publisher={Elsevier}, author={Campbell, Stephen L.}, editor={Byrnes, C. I. and Lindquist, A.Editors}, year={1986}, pages={313–318} }
 @article{campbell_1986, title={Countability of Sets}, volume={93}, ISSN={0002-9890 1930-0972}, url={http://dx.doi.org/10.1080/00029890.1986.11971864}, DOI={10.1080/00029890.1986.11971864}, number={6}, journal={The American Mathematical Monthly}, publisher={Informa UK Limited}, author={Campbell, Stephen L.}, year={1986}, month={Jun}, pages={480–481} }
 @article{campbell_1986, title={Index two linear time varying singular systems of differential equations}, volume={5}, ISSN={0278-081X 1531-5878}, url={http://dx.doi.org/10.1007/bf01600189}, DOI={10.1007/bf01600189}, number={1}, journal={Circuits, Systems, and Signal Processing}, publisher={Springer Science and Business Media LLC}, author={Campbell, Stephen L.}, year={1986}, month={Mar}, pages={97–107} }
 @book{campbell_1986, title={Progress Report Number 2 on Contract AFOSR-84-0240.}, DOI={10.21236/ada172881}, abstractNote={Abstract : Implicit systems of differential equations of the form F(t,y,y') = 0 naturally arise in many circuit and control problems, economic models, and the solution of partial differential equations by the method of lines. Implicit systems are also called singular, differential-algebraic, semi-state, constrained, and descriptor. The theory is well understood, and numerical codes exist, for index zero, index one, and linear constant coefficient problems. Higher index systems occur in circuit and control problems. The numerical and analytic behavior of such higher index systems is not well understood and is incomplete. It has recently been shown that traditional methods, such as backward differences, need not work on higher index systems. Good characterizations of the solution manifold are often difficult to obtain. This research project is to study the numerical and analytic solution of higher index implicit differential equations. Applications will be made to circuit theory, control theory, and the analysis of numerically ill-conditioned index one systems.}, institution={Defense Technical Information Center}, author={Campbell, Stephen L.}, year={1986}, month={Jan} }
 @article{campbell_rodriguez_1985, title={Bounded solutions of discrete singular systems on infinite time intervals}, volume={30}, ISSN={0018-9286 1558-2523}, url={http://dx.doi.org/10.1109/tac.1985.1103905}, DOI={10.1109/tac.1985.1103905}, abstractNote={This paper concerns noncausal, nonlinear discrete singular systems of the formaX_{k+1} + Bx_{k} = m[x]_{k}on the infinite intervali = [0, 1, --.]for some causal, nonlinear time variable operatorsm. Existence theorems for bounded solutions are given. Methods for estimating the infinite time problem by a finite time problem are developed.}, number={2}, journal={IEEE Transactions on Automatic Control}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Campbell, S. and Rodriguez, J.}, year={1985}, month={Feb}, pages={165–168} }
 @misc{campbell_1985, title={Rank deficient least squares and the numerical solution of linear singular implicit systems of differential equations}, ISBN={9780821850411 9780821876329}, ISSN={1098-3627 0271-4132}, url={http://dx.doi.org/10.1090/conm/047/828292}, DOI={10.1090/conm/047/828292}, journal={Linear algebra and its role in systems theory}, publisher={American Mathematical Society}, author={Campbell, Stephen L.}, year={1985}, pages={51–63} }
 @article{campbell_1985, title={The Numerical Solution of Higher Index Linear Time Varying Singular Systems of Differential Equations}, volume={6}, ISSN={0196-5204 2168-3417}, url={http://dx.doi.org/10.1137/0906024}, DOI={10.1137/0906024}, abstractNote={A family of Taylor-type methods is given for solving numerically a large class of singular systems of differential equations of the form $A(t)x'(t) + B(t)x(t) = f(t)$. The advantages, disadvantages, and implementation of these methods are discussed and several analytical and numerical examples are given.}, number={2}, journal={SIAM Journal on Scientific and Statistical Computing}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Campbell, Stephen L.}, year={1985}, month={Apr}, pages={334–348} }
 @inproceedings{campbell_1984, title={Explicit methods for solving singular differential equation systems}, booktitle={Proceedings of the 27th Midwest Symposium on Circuits and Systems}, author={Campbell, Stephen L.}, year={1984}, pages={696–699} }
 @inproceedings{campbell_1984, title={Non-BDF methods for the solution of time varying implicit differential equations}, volume={21}, DOI={10.1109/ACC.1984.4171500}, booktitle={Proceedings of the 1984 American Control Conference}, author={Campbell, Stephen L.}, year={1984}, pages={1315–1318} }
 @inproceedings{campbell_rodriguez_1984, title={Nonlinear singular systems and contraction mappings}, volume={21}, DOI={10.1109/ACC.1984.4171540}, booktitle={Proceedings of the 1984 American Control Conference}, author={Campbell, Stephen L. and Rodriguez, J.}, year={1984}, pages={1513–1519} }
 @inproceedings{campbell_1984, title={Nonlinear time-varying generalized state-space systems: An overview}, url={http://dx.doi.org/10.1109/cdc.1984.272332}, DOI={10.1109/cdc.1984.272332}, abstractNote={This paper will review the current literature on nonlinear and time varying generalized state-space systems of the form F(t,y,y') = O.}, booktitle={The 23rd IEEE Conference on Decision and Control}, publisher={IEEE}, author={Campbell, Stephen}, year={1984}, month={Dec} }
 @article{campbell_1984, title={On using orthogonal functions with singular systems}, volume={131}, number={6}, journal={IEE Proceedings D-Control Theory & Applications}, author={Campbell, Stephen L.}, year={1984}, pages={267–268} }
 @article{campbell_1984, title={Regularizations of linear time varying singular systems}, volume={20}, ISSN={0005-1098}, url={http://dx.doi.org/10.1016/0005-1098(84)90052-9}, DOI={10.1016/0005-1098(84)90052-9}, abstractNote={Singular systems of differential equations arising in reduced-order models are often regularized by the introduction of small parameters. The types of regularization used for linear time invariant systems need not work on linear time varying systems. This paper gives examples and discusses this behavior. Conditions under which the standard type of regularization works are developed.}, number={3}, journal={Automatica}, publisher={Elsevier BV}, author={Campbell, Stephen L.}, year={1984}, month={May}, pages={365–370} }
 @article{campbell_1984, title={Review of polynomials and linear control systems, by Stephen Barnett}, volume={61}, DOI={10.1016/0024-3795(84)90038-7}, journal={Linear Algebra and its Applications}, publisher={Elsevier BV}, author={Campbell, Stephen L.}, year={1984}, month={Sep}, pages={289–290} }
 @article{campbell_1984, title={The numerical solution of differential algebraic equation systems}, volume={14}, number={1}, journal={All About Simulators}, author={Campbell, Stephen L.}, editor={Amico, V. and Clymer, A.Editors}, year={1984}, pages={7–12} }
 @article{campbell_petzold_1983, title={Canonical Forms and Solvable Singular Systems of Differential Equations}, volume={4}, ISSN={0196-5212 2168-345X}, url={http://dx.doi.org/10.1137/0604051}, DOI={10.1137/0604051}, abstractNote={In this paper we investigate the relationship between solvability and the existence of canonical forms for the linear system of differential equations $E ( t ) x' ( t ) + F ( t ) x ( t ) = f ( t )$. We show that if E, F are analytic on the interval $[ 0 \,\, T ]$, then the differential equation is solvable if and only if it can be put into a certain canonical form. We give examples to show that this is not true if E, F are only differentiable.}, number={4}, journal={SIAM Journal on Algebraic Discrete Methods}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Campbell, Stephen L. and Petzold, Linda R.}, year={1983}, month={Dec}, pages={517–521} }
 @article{campbell_1983, title={Consistent initial conditions for singular nonlinear systems}, volume={2}, ISSN={0278-081X 1531-5878}, url={http://dx.doi.org/10.1007/bf01598143}, DOI={10.1007/bf01598143}, number={1}, journal={Circuits, Systems, and Signal Processing}, publisher={Springer Science and Business Media LLC}, author={Campbell, Stephen L.}, year={1983}, month={Mar}, pages={45–55} }
 @article{campbell_1983, title={Index Two Linear Time-Varying Singular Systems of Differential Equations}, volume={4}, ISSN={0196-5212 2168-345X}, url={http://dx.doi.org/10.1137/0604026}, DOI={10.1137/0604026}, abstractNote={Linear time varying singular systems of differential equations of the formA(t)x′(t) + B(t)x(t)=f(t) whereA(t) is singular and the system has index at most two are considered. Recent results on their analytic solution are improved on. Examples are given that show these results are not easily extended.}, number={2}, journal={SIAM Journal on Algebraic Discrete Methods}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Campbell, Stephen L.}, year={1983}, month={Jun}, pages={237–243} }
 @article{barker_campbell_1983, title={Internal stability of two dimensional systems}, volume={14}, ISSN={0308-1087 1563-5139}, url={http://dx.doi.org/10.1080/03081088308817572}, DOI={10.1080/03081088308817572}, abstractNote={Let A1 and A2 be n×n matrices with numerical radii . We show that if , then zero is not an eigenvalue of for any complex numbers z1 and z2 of modulus 1. We also show by examples and by a general proposition that for non-normal matrices the numerical radius cannot be replaced by the spectral radius.}, number={4}, journal={Linear and Multilinear Algebra}, publisher={Informa UK Limited}, author={Barker, George Phillip and Campbell, Stephen L.}, year={1983}, month={Dec}, pages={365–369} }
 @inproceedings{campbell_1983, title={Multiparameter singular systems: Nondissective approaches}, url={http://dx.doi.org/10.1109/cdc.1983.269733}, DOI={10.1109/cdc.1983.269733}, abstractNote={Singular systems of differential equations of the form Ax' + Bx = f are considered. The difference between the dissective or deflation approachs and derivative loading are discussed. Examples are given to show how derivative loading can sometimes be helpful in analyzing multiparameter systems.}, booktitle={The 22nd IEEE Conference on Decision and Control}, publisher={IEEE}, author={Campbell, Stephen}, year={1983} }
 @article{campbell_1983, title={One canonical form for higher-index linear time-varying singular systems}, volume={2}, ISSN={0278-081X 1531-5878}, url={http://dx.doi.org/10.1007/bf01599073}, DOI={10.1007/bf01599073}, number={3}, journal={Circuits, Systems, and Signal Processing}, publisher={Springer Science and Business Media LLC}, author={Campbell, Stephen L.}, year={1983}, month={Sep}, pages={311–326} }
 @inbook{campbell_1983, place={Pitman}, title={Recent applications of generalized inverses}, booktitle={Recent Applications of Generalized Inverses}, author={Campbell, Stephen L.}, year={1983}, pages={1–11} }
 @article{campbell_1983, title={The Drazln inverse and systems of second order linear differential equations}, volume={14}, ISSN={0308-1087 1563-5139}, url={http://dx.doi.org/10.1080/03081088308817556}, DOI={10.1080/03081088308817556}, abstractNote={The problem of computing the Drazin inverse of the matrix discussed. The relationship of this problem to second order differential equations is explained and known results given.}, number={2}, journal={Linear and Multilinear Algebra}, publisher={Informa UK Limited}, author={Campbell, Stephen L.}, year={1983}, month={Oct}, pages={195–198} }
 @article{campbell_rose_1982, title={A second order singular linear system arising in electric power systems analysis†}, volume={13}, ISSN={0020-7721 1464-5319}, url={http://dx.doi.org/10.1080/00207728208926334}, DOI={10.1080/00207728208926334}, abstractNote={Abstract The linear system Mx¨ + (∝ M+ β) K)[xacute] + KX= F with M singular, is decomposed into two linear systems, one singular and one non-singular. The singular ono is solved explicitly in terms of M, K, f, a, S and analysed.}, number={1}, journal={International Journal of Systems Science}, publisher={Informa UK Limited}, author={Campbell, Stephen L. and Rose, Nicholas J.}, year={1982}, month={Jan}, pages={101–108} }
 @article{campbell_1982, title={Nontrivial isometries on sp(α)}, volume={5}, ISSN={0161-1712 1687-0425}, url={http://dx.doi.org/10.1155/s0161171282000222}, DOI={10.1155/s0161171282000222}, abstractNote={sp(α)is a Banach space of sequencesxwith‖x‖=(∑i=0∞|xi|p+α∑i=0∞|xi+1−xi|p)1/p. For1<p<∞,p≠2,0<α<∞,α≠1, there are no nontrivial surjective isometries insp(α). It has been conjectured that there are no nontrivial isometries. This note gives two distinct counterexamples to this conjecture and a partial affirmative answer for the case of isometries with finite codimension.}, number={2}, journal={International Journal of Mathematics and Mathematical Sciences}, publisher={Hindawi Limited}, author={Campbell, Stephen L.}, year={1982}, pages={257–261} }
 @article{campbell_1982, title={On positive controllers and linear quadratic optimal control problems†}, volume={36}, ISSN={0020-7179 1366-5820}, url={http://dx.doi.org/10.1080/00207178208932938}, DOI={10.1080/00207178208932938}, abstractNote={An assumption on the non-negative solutions of quadratic equations has been used to study linear quadratic optimal control problems with positive controllers. This note investigates this assumption in more detail.}, number={5}, journal={International Journal of Control}, publisher={Informa UK Limited}, author={Campbell, Stephen L.}, year={1982}, month={Nov}, pages={885–888} }
 @inbook{campbell_1982, series={Pitman Advanced Publishing Program}, title={The Drazin inverse of an operator}, booktitle={Recent Applications of Generalized Inverses}, publisher={Pitman Publishing Company}, author={Campbell, S.L.}, editor={Campbell, S.L.Editor}, year={1982}, collection={Pitman Advanced Publishing Program} }
 @article{campbell_1981, title={A more singular singularly perturbed linear system}, volume={26}, ISSN={0018-9286}, url={http://dx.doi.org/10.1109/tac.1981.1102614}, DOI={10.1109/tac.1981.1102614}, abstractNote={The singularly perturbed linear system A(\epsilon)\dot{x}+B(\epsilon)x=f(\epsilon, t) is studied. The matrix A(\epsilon) is allowed to be singular not only for \epsilon=0 , but for \epsilon > 0 .}, number={2}, journal={IEEE Transactions on Automatic Control}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Campbell, S.}, year={1981}, month={Apr}, pages={507–510} }
 @article{campbell_silverstein_1981, title={A nonlinear system with singular vector field near equilibria}, volume={12}, ISSN={0003-6811 1563-504X}, url={http://dx.doi.org/10.1080/00036818108839348}, DOI={10.1080/00036818108839348}, abstractNote={The system Nω=(N-α)ω+y, N= bN+aωωT, N(t)∊Rm×m, ω(t)∊Rm which originally arose from a model for the pathological behavior of neural networks, is studied. Similar equations can arise in a variety of applications. It is shown that if N(0) is positive definite, then solutions exist for all time. Equilibrium points are determined. N is found to be singular at the equilibrium points, making the analysis of the asymptotic properties of the system non-trivial. The asymptotic behavior when y = 0 is completely described. Some results are proven on the asymptotic behavior of N and ω when y≠0}, number={1}, journal={Applicable Analysis}, publisher={Informa UK Limited}, author={Campbell, Stephen L. and Silverstein, Jack W.}, year={1981}, month={Jan}, pages={57–71} }
 @article{campbell_1981, title={A procedure for analyzing a class of nonlinear semistate equations that arise in circuit and control problems}, volume={28}, ISSN={0098-4094}, url={http://dx.doi.org/10.1109/tcs.1981.1084966}, DOI={10.1109/tcs.1981.1084966}, abstractNote={Some circuits not possessing a state-variable represenation may admit semistate equations of the form Ax(t)+B(x(t))=f(t) where x , f are vector functions, A is a singular constant matrix, and B is a nonlinear vector valued function. Some nonlinear optimal control problems, in which certain combinations of controls are either "cheap" or free, also lead to equations in this form. In this paper we show how In many cases of interest It is possible to solve a singular linear subsystem and use this solution to reduce the problem to a smaller order nonsingular, nonlinear system.}, number={3}, journal={IEEE Transactions on Circuits and Systems}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Campbell, S.}, year={1981}, month={Mar}, pages={256–261} }
 @article{campbell_poole_1981, title={Computing nonnegative rank factorizations}, volume={35}, ISSN={0024-3795}, url={http://dx.doi.org/10.1016/0024-3795(81)90272-x}, DOI={10.1016/0024-3795(81)90272-x}, abstractNote={The existence of nonnegative generalized inverses in terms of nonnegative rank factorizations is considered. An algorithm is presented which computes a nonnegative rank factorization of a nonnegative matrix when a nonnegative 1-inverse exists.}, journal={Linear Algebra and its Applications}, publisher={Elsevier BV}, author={Campbell, Stephen L. and Poole, George D.}, year={1981}, month={Feb}, pages={175–182} }
 @article{campbell_poole_1981, title={Convergent regular splittings for nonnegative matrices}, volume={10}, ISSN={0308-1087 1563-5139}, url={http://dx.doi.org/10.1080/03081088108817393}, DOI={10.1080/03081088108817393}, abstractNote={MP matrices are those real matrices which possess a nonnegative, nonsingular l-inverse. This paper characterizes the nonnegative MP matrices and hence, determines when a nonnegative matrix A has a convergent regular splitting M—Q which induces the linear stationary iterative scheme x k+1=M −1 Qxk +M −1 b to solve Ax=b.}, number={1}, journal={Linear and Multilinear Algebra}, publisher={Informa UK Limited}, author={Campbell, Stephen L. and Poole, George D.}, year={1981}, month={Feb}, pages={63–73} }
 @inproceedings{campbell_1981, title={Numerical procedures for analyzing nonlinear semi-state equations}, booktitle={Proceedings Fifth International Symposium on the Mathematical Theory of Networks and Systems}, author={Campbell, Stephen L.}, year={1981}, pages={22–27} }
 @article{campbell_1981, title={On an assumption guaranteeing boundary layer convergence of singularly perturbed systems}, volume={17}, ISSN={0005-1098}, url={http://dx.doi.org/10.1016/0005-1098(81)90038-8}, DOI={10.1016/0005-1098(81)90038-8}, abstractNote={In a recent paper by B. A. Francis, an assumption was made that guaranteed convergence in the boundary layer for singularly perturbed linear systems, but the assumption was not discussed. This note examines this assumption in some detail. Verifiable sufficient and necessary conditions are given. Illustrative examples are presented.}, number={4}, journal={Automatica}, publisher={Elsevier BV}, author={Campbell, Stephen L.}, year={1981}, month={Jul}, pages={645–646} }
 @article{campbell_clark_1981, title={Order and the index of singular time-invariant linar systems}, volume={1}, ISSN={0167-6911}, url={http://dx.doi.org/10.1016/s0167-6911(81)80048-5}, DOI={10.1016/s0167-6911(81)80048-5}, abstractNote={Various concepts of order have been proposed in the literature. It is shown that many of these are directly related to the index of a system.}, number={2}, journal={Systems & Control Letters}, publisher={Elsevier BV}, author={Campbell, Stephen L. and Clark, Kenneth}, year={1981}, month={Aug}, pages={119–122} }
 @article{campbell_1980, title={Continuity of The Drazin inverse}, volume={8}, ISSN={0308-1087 1563-5139}, url={http://dx.doi.org/10.1080/03081088008817329}, DOI={10.1080/03081088008817329}, abstractNote={Let A be an n×n matrix. It is shown that if a matrix  comes close to satisfying the definition of the Drazin inverse of A,AD , then  is close to AD .}, number={3}, journal={Linear and Multilinear Algebra}, publisher={Informa UK Limited}, author={Campbell, Stephen L.}, year={1980}, month={Feb}, pages={265–268} }
 @article{campbell_1980, title={Linear operators for which T*T and TT* commute III}, volume={91}, number={1}, journal={Pacific Journal of Mathematics}, author={Campbell, Stephen L.}, year={1980}, pages={39–45} }
 @article{campbell_faulkner_1980, title={Operators on Banach spaces with complemented ranges}, volume={35}, ISSN={0001-5954 1588-2632}, url={http://dx.doi.org/10.1007/bf01896831}, DOI={10.1007/bf01896831}, number={1-2}, journal={Acta Mathematica Academiae Scientiarum Hungaricae}, publisher={Springer Science and Business Media LLC}, author={Campbell, S. L. and Faulkner, G. D.}, year={1980}, month={Mar}, pages={123–128} }
 @article{campbell_1980, title={Singular linear systems of differential equations with delays}, volume={11}, ISSN={0003-6811 1563-504X}, url={http://dx.doi.org/10.1080/00036818008839326}, DOI={10.1080/00036818008839326}, abstractNote={The differential equation Ax + Bx = Cx(t-l) + f is studied where A, B, C are square matrices. All matrices are allowed to be singular. Examples are given to show that not all initial functions are consistent and that for consistent initial conditions, solutions may be continuous for only a finite time period. Solutions are given explicitly by a recursion formula and consistent initial conditions are explicitly characterized}, number={2}, journal={Applicable Analysis}, publisher={Informa UK Limited}, author={Campbell, Stephen L.}, year={1980}, month={Jan}, pages={129–136} }
 @inproceedings{campbell_1979, title={A functional analytic approach to autonomous linear singular perturbation problems}, booktitle={Proceedings of the Seventeenth Annual Allerton Conference on Communication, Control, and Computing}, author={Campbell, Stephen L.}, year={1979}, pages={445–463} }
 @article{campbell_faulkner_gardner_1979, title={Isometries on L^p Spaces and Copies of L^p shifts}, volume={77}, ISSN={0002-9939 1088-6826}, DOI={10.2307/2042638}, number={2}, journal={Proceedings of the American Mathematical Society}, author={Campbell, Stephen L. and Faulkner, G.D. and Gardner, M.L.}, year={1979}, month={Nov}, pages={198–200} }
 @inbook{campbell_faulkner_sine_1979, place={San Francisco, California}, series={Research notes in mathematics}, title={Isometries, projections and Wold decompositions}, ISBN={9780822484509 9780273084501}, booktitle={Operator Theory and Functional Analysis}, publisher={Pitman Publishing Company}, author={Campbell, Stephen L. and Faulkner, G.D. and Sine, Robert}, editor={Erdelyi, IvanEditor}, year={1979}, pages={84–114}, collection={Research notes in mathematics} }
 @article{campbell_1979, title={Limit behavior of solutions of singular difference equations}, volume={23}, ISSN={0024-3795}, url={http://dx.doi.org/10.1016/0024-3795(79)90100-9}, DOI={10.1016/0024-3795(79)90100-9}, abstractNote={Necessary and sufficient conditions for a solution {zk} of the difference equation Azk+1+Bzk = b, k ⩾0, with A singular, to be a convergent sequence of vectors are given under a variety of assumptions. Theoretical results on iterative schemes for solving Ax = b by singular splittings, A = A+B, are given first. In particular, the case when A = A∗ and A is positive semi-definite is considered. Then applications to discrete control problems and backwards population projection are discussed.}, journal={Linear Algebra and its Applications}, publisher={Elsevier BV}, author={Campbell, Stephen L.}, year={1979}, month={Feb}, pages={167–178} }
 @article{campbell_1979, title={Nonregular Singular Dynamic Leontief Systems}, volume={47}, ISSN={0012-9682}, url={http://dx.doi.org/10.2307/1914020}, DOI={10.2307/1914020}, number={6}, journal={Econometrica}, publisher={JSTOR}, author={Campbell, Stephen L.}, year={1979}, month={Nov}, pages={1565} }
 @article{campbell_1979, title={On a singularly perturbed autonomous linear control problem}, volume={24}, ISSN={0018-9286}, url={http://dx.doi.org/10.1109/tac.1979.1101951}, DOI={10.1109/tac.1979.1101951}, abstractNote={A singularly perturbed autonomous control process is examined. The relationship between the original and the reduced problem is developed.}, number={1}, journal={IEEE Transactions on Automatic Control}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Campbell, S.}, year={1979}, month={Feb}, pages={115–117} }
 @article{campbell_rose_1979, title={Singular Perturbation of Autonomous Linear Systems}, volume={10}, ISSN={0036-1410 1095-7154}, url={http://dx.doi.org/10.1137/0510051}, DOI={10.1137/0510051}, abstractNote={Let $X_\varepsilon (t) = \exp (({{A + B} /\varepsilon })t)$ where A, B are $n \times n$ matrices. It is shown that $X_\varepsilon (t)$ converges pointwise for $t > 0$ as $\varepsilon \to 0^ + $ if and only if Index $B \leqq 1$ and the nonzero eigenvalues of B have negative real part. An explicit representation of the limit of $X_\varepsilon (t)$ is given. These results are applied to the singularly perturbed system $\dot x = A_1 (\varepsilon )x + A_2 (\varepsilon )y$, $\varepsilon \dot y = B_1 (\varepsilon )x + B_2 (\varepsilon )y$. This paper differs from earlier work both in the derivation of necessary and sufficient conditions and in the explicit forms for the limits.}, number={3}, journal={SIAM Journal on Mathematical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Campbell, Stephen L. and Rose, Nicholas J.}, year={1979}, month={May}, pages={542–551} }
 @article{campbell_daughtry_1979, title={The stable solutions of quadratic matrix equations}, volume={74}, number={1}, journal={Proceedings of the American Mathematical Society}, author={Campbell, Stephen L. and Daughtry, John}, year={1979}, pages={19–23} }
 @article{campbell_1978, title={Linear operators for which T∗T and T + T∗ commute. III}, volume={76}, ISSN={0030-8730 0030-8730}, url={http://dx.doi.org/10.2140/pjm.1978.76.17}, DOI={10.2140/pjm.1978.76.17}, number={1}, journal={Pacific Journal of Mathematics}, publisher={Mathematical Sciences Publishers}, author={Campbell, Stephen}, year={1978}, month={May}, pages={17–19} }
 @article{campbell_gupta_1978, title={On k-quasihyponormal operators}, volume={23}, journal={Mathematica Japonica}, author={Campbell, Stephen L. and Gupta, B.C.}, year={1978}, pages={185–189} }
 @article{campbell_1978, title={On the limit of a product of matrix exponentials}, volume={6}, ISSN={0308-1087 1563-5139}, url={http://dx.doi.org/10.1080/03081087808817221}, DOI={10.1080/03081087808817221}, abstractNote={The existence of the limit as ϵ→0 exp[(A+B/ϵ)t] exp[-Bt/ϵ]is studied for n×n matrices A,B. Necessary and sufficient conditions on B that the limit exist for all A are given.}, number={1}, journal={Linear and Multilinear Algebra}, publisher={Informa UK Limited}, author={Campbell, Stephen L.}, year={1978}, month={Jan}, pages={55–59} }
 @article{campbell_1978, title={Optimal control of discrete linear processes with quadratic cost}, volume={9}, ISSN={0020-7721 1464-5319}, url={http://dx.doi.org/10.1080/00207727808941742}, DOI={10.1080/00207727808941742}, abstractNote={A direct method 18 given for solving the optimal control problem Xk+1+ Bukk=0,,N — l with quadratic cost functional. The matrices A, B,,Q, H are all allowed to be singular. The process is not assumed to be completely controllable. The coefficients are assumed to have the property that there exists a scalar μ such that Q + B ∗( — μA∗+I)−1-μH(μ — A)−1 B is invertible.}, number={8}, journal={International Journal of Systems Science}, publisher={Informa UK Limited}, author={Campbell, Stephen L.}, year={1978}, month={Aug}, pages={841–847} }
 @article{campbell_rose_1978, title={Singular perturbation of autonomous linear systems III}, volume={44}, journal={Houston Journal of Mathematics}, author={Campbell, Stephen L. and Rose, N.J.}, year={1978}, pages={527–539} }
 @article{campbell_1978, title={Singular perturbation of autonomous linear systems, II}, volume={29}, ISSN={0022-0396}, url={http://dx.doi.org/10.1016/0022-0396(78)90046-3}, DOI={10.1016/0022-0396(78)90046-3}, abstractNote={This paper is concerned with determining the limit of exp(A + Bϵ + Cϵr + Eϵs)t for t > 0, where A, B, C, E are n × n complex matrices, and s > r > 1. Explicit expressions are derived for the limit under a variety of assumptions. Examples are given to justify some of these assumptions. The application of these limit theorems to singularly perturbed antonomous linear systems is discussed.}, number={3}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Campbell, Stephen L}, year={1978}, month={Sep}, pages={362–373} }
 @article{campbell_meyer_1978, title={Weak Drazin inverses}, volume={20}, ISSN={0024-3795}, url={http://dx.doi.org/10.1016/0024-3795(78)90048-4}, DOI={10.1016/0024-3795(78)90048-4}, abstractNote={A new type of generalized inverse is defined which is a weakened form of the Drazin inverse. These new inverses are called (d)-inverses. Basic properties of (d)-inverses are developed. It is shown that (d)-inverses are often easier to compute than Drazin inverses and can frequently be used in place of the Drazin inverse when studying systems of differential equations with singular coefficients or when studying Marcov chains.}, number={2}, journal={Linear Algebra and its Applications}, publisher={Elsevier BV}, author={Campbell, Stephen L. and Meyer, Carl D., Jr.}, year={1978}, pages={167–178} }
 @article{campbell_1977, title={Linear Systems of Differential Equations with Singular Coefficients}, volume={8}, ISSN={0036-1410 1095-7154}, url={http://dx.doi.org/10.1137/0508081}, DOI={10.1137/0508081}, abstractNote={Differential equations of the form $A\dot x + Bx = f$ are studied where A, B are $m \times n$ matrices. Explicit solutions are derived for several cases of interest. One such case is when there exists a scalar $\lambda $ such that $\lambda A + B$ is of full rank. Another includes the case when A, B are normal matrices and one is positive semidefinite. The application of these results to linear autonomous control processes is discussed.}, number={6}, journal={SIAM Journal on Mathematical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Campbell, Stephen L.}, year={1977}, month={Nov}, pages={1057–1066} }
 @article{campbell_geller_1977, title={Linear operators for which T*T and T+T* commute II}, volume={226}, journal={Transactions of the American Mathematical Society}, author={Campbell, Stephen L. and Geller, R.}, year={1977}, pages={305–319} }
 @article{campbell_gellar_1977, title={On asymptotic properties of several classes of operators}, volume={66}, number={1}, journal={Proceedings of the American Mathematical Society}, author={Campbell, Stephen L. and Gellar, R.}, year={1977}, pages={79–84} }
 @article{campbell_1977, title={On continuity of the Moore-Penrose and Drazin generalized inverses}, volume={18}, ISSN={0024-3795}, url={http://dx.doi.org/10.1016/0024-3795(77)90079-9}, DOI={10.1016/0024-3795(77)90079-9}, abstractNote={Let A be an m × n matrix. It is shown that if a matrix comes close to satisfying the definition of the Moore-Penrose generalized inverse of A,A†, then ┆–A†┆ is small. Norm estimates are given which make precise what is close. The Drazin generalized inverse is also considered.}, number={1}, journal={Linear Algebra and its Applications}, publisher={Elsevier BV}, author={Campbell, Stephen L.}, year={1977}, pages={53–57} }
 @article{campbell_meyer, jr._rose_1976, title={Applications of the Drazin Inverse to Linear Systems of Differential Equations with Singular Constant Coefficients}, volume={31}, ISSN={0036-1399 1095-712X}, url={http://dx.doi.org/10.1137/0131035}, DOI={10.1137/0131035}, abstractNote={Let A, B be $n \times n$ matrices, f a vector-valued function. A and B may both be singular. The differential equation $Ax' + Bx = f$ is studied utilizing the theory of the Drazin inverse. A closed form for all solutions of the differential equation is given when the equation has unique solutions for consistent initial conditions.}, number={3}, journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Campbell, Stephen L. and Meyer, Jr., Carl D. and Rose, Nicholas J.}, year={1976}, month={Nov}, pages={411–425} }
 @article{campbell_1976, title={Differentiation of the Drazin Inverse}, volume={30}, ISSN={0036-1399 1095-712X}, url={http://dx.doi.org/10.1137/0130062}, DOI={10.1137/0130062}, abstractNote={Suppose that A is an $n \times n$ matrix of differentiable functions. Suppose that $A^D $ is defined as $A^D (t) = [ {A(t)} ]^D $ , where $[ {A(t)} ]^D $ is the Drazin inverse of the $n \times n$ matrix $A(t)$. A formula is derived for the derivative of $A^D $ in terms of A, $A^D $ and the derivative of A. The conditions under which $A^D $ is differentiable are discussed.}, number={4}, journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Campbell, Stephen L.}, year={1976}, month={Jun}, pages={703–707} }
 @article{campbell_1976, title={Optimal Control of Autonomous Linear Processes with Singular Matrices in the Quadratic Cost Functional}, volume={14}, ISSN={0363-0129 1095-7138}, url={http://dx.doi.org/10.1137/0314068}, DOI={10.1137/0314068}, abstractNote={The optimal control of the autonomous linear process $\dot x = Ax + Bu$ with quadratic cost functional is studied. The initial and terminal times and positions are fixed. The matrices in the cost functional are allowed to be singular. An assumption, weaker than invertibility, is placed on the coefficient matrices. Under this assumption, necessary and sufficient conditions are given for the existence of an optimal control in terms of the initial and final position of the process. A closed form for the optimal control is given.}, number={6}, journal={SIAM Journal on Control and Optimization}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Campbell, Stephen L.}, year={1976}, month={Nov}, pages={1092–1106} }
 @inproceedings{campbell_1976, title={Optimal control of autonomous linear processes with singular matrices in the quadratic cost functional II}, url={http://dx.doi.org/10.1109/cdc.1976.267733}, DOI={10.1109/cdc.1976.267733}, abstractNote={The optimal control of the autonomous linear process X = Ax + Bu with quadratic cost functional is studied. Initial and terminal times and positions are fixed. An assumption, weaker than invertibility, is placed on the matrices involved. A closed form for the optimal control is given. The extension of the method to other problems is discussed, including infinite systems and discrete problems.}, booktitle={1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes}, publisher={IEEE}, author={Campbell, S.}, year={1976}, month={Dec} }
 @article{campbell_geller_1976, title={Spectral properties of linear operators for which T*T and T + T* commute}, volume={60}, number={1}, journal={Proceedings of the American Mathematical Society}, author={Campbell, Stephen L. and Geller, R.}, year={1976}, pages={197–202} }
 @article{campbell_1976, title={The Drazin Inverse of an Infinite Matrix}, volume={31}, ISSN={0036-1399 1095-712X}, url={http://dx.doi.org/10.1137/0131043}, DOI={10.1137/0131043}, abstractNote={Let $A = [ {a_{ij} } ]$, $0\leqq i < \infty $, $0\leqq j < \infty $. Then A is called a denumerably infinite matrix. A way to define a Drazin inverse for A is presented. The application of this definition to denumerable Markov chains, infinite linear systems of differential equations, and linear operators on Banach spaces is discussed.}, number={3}, journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Campbell, Stephen L.}, year={1976}, month={Nov}, pages={492–503} }
 @article{campbell_meyer_1975, title={Continuity properties of the Drazin pseudoinverse}, volume={10}, ISSN={0024-3795}, url={http://dx.doi.org/10.1016/0024-3795(75)90097-x}, DOI={10.1016/0024-3795(75)90097-x}, abstractNote={Let BD denote that Drazin inverse of the n×n complex matrix B. Define the core-rank of B as rank (Bi(B)) where i(B) is the index of B. Let j = 1,2,…, and Aj and A be square matrices such that Ai converges to A with respect to some norm. The main result of this paper is that AjD converges to AD if and only if there exist a j0 such that core-rank Aj=core-rankA for j ⩾ j0.}, number={1}, journal={Linear Algebra and its Applications}, publisher={Elsevier BV}, author={Campbell, Stephen L. and Meyer, Carl D., Jr.}, year={1975}, month={Feb}, pages={77–83} }
 @article{campbell_meyer_1975, title={EP Operators and Generalized Inverses}, volume={18}, ISSN={0008-4395 1496-4287}, url={http://dx.doi.org/10.4153/cmb-1975-061-4}, DOI={10.4153/cmb-1975-061-4}, abstractNote={AbstractThe relationship between properties of the generalized inverse of A, A†, and of the adjoint of A, A*, are studied. The property that A†A and AA† commute, called (E4), is investigated. (E4) generalizes the property of A being EPr. A canonical form and a formula for A† are given if a matrix A is (E4). Results are in a Hilbert space setting whenever possible. Examples are given.}, number={3}, journal={Canadian Mathematical Bulletin}, publisher={Canadian Mathematical Society}, author={Campbell, Stephen L. and Meyer, Carl D.}, year={1975}, month={Aug}, pages={327–333} }
 @article{campbell_1975, title={Linear operators for which T∗T and T + T∗ commute}, volume={61}, ISSN={0030-8730 0030-8730}, url={http://dx.doi.org/10.2140/pjm.1975.61.53}, DOI={10.2140/pjm.1975.61.53}, number={1}, journal={Pacific Journal of Mathematics}, publisher={Mathematical Sciences Publishers}, author={Campbell, Stephen}, year={1975}, month={Nov}, pages={53–57} }
 @article{campbell_1975, title={Operator-valued inner functions analytic on the closed disc. II}, volume={60}, ISSN={0030-8730 0030-8730}, url={http://dx.doi.org/10.2140/pjm.1975.60.37}, DOI={10.2140/pjm.1975.60.37}, abstractNote={An operator-valued inner function V is called scalar if {V(w): I w I < 1} is a commuting family of normal operators.Suppose that T is a bounded linear operator with || T\\ ^ 1 and spectral radius strictly less than one.Let V τ be its Potapov inner function and define U τ = V τ Vj{ί).The structure of nonnormal T for which U τ is scalar is discussed.An explicit characterization is given if the underlying Hubert space is finite dimensional.Examples are given for the infinite dimensional case.The relationship between scalar inner functions and operators for which T*T and T* + T commute is examined.}, number={2}, journal={Pacific Journal of Mathematics}, publisher={Mathematical Sciences Publishers}, author={Campbell, Stephen}, year={1975}, month={Oct}, pages={37–49} }
 @article{campbell_1975, title={Subnormal operators with nontrivial quasinormal extensions}, volume={37}, number={3-4}, journal={Acta Scientiarum Mathematicarum}, author={Campbell, Stephen L.}, year={1975}, pages={191–193} }
 @article{campbell_1974, title={Commutation properties of the coefficient matrix in the differential equation of an inner function}, volume={42}, number={2}, journal={Proceedings of the American Mathematical Society}, author={Campbell, Stephen L.}, year={1974}, pages={507–512} }
 @article{campbell_1974, title={Linear operators for which T∗T and TT∗ commute. II}, volume={53}, ISSN={0030-8730 0030-8730}, url={http://dx.doi.org/10.2140/pjm.1974.53.355}, DOI={10.2140/pjm.1974.53.355}, number={2}, journal={Pacific Journal of Mathematics}, publisher={Mathematical Sciences Publishers}, author={Campbell, Stephen}, year={1974}, month={Aug}, pages={355–361} }
 @article{carmpbell_1972, title={Inner functions analytic at a point}, volume={16}, ISSN={0019-2082}, url={http://dx.doi.org/10.1215/ijm/1256065547}, DOI={10.1215/ijm/1256065547}, number={4}, journal={Illinois Journal of Mathematics}, publisher={Duke University Press}, author={Carmpbell, Stephen L.}, year={1972}, month={Dec}, pages={651–652} }
 @article{campbell_1972, title={Linear operators for which T*T and TT* commute}, volume={34}, journal={Proc. American Mathematical Society}, author={Campbell, Stephen L.}, year={1972}, pages={177–180} }
 @article{campbell_1972, title={Operator-valued inner functions analytic on the closed disc}, volume={41}, ISSN={0030-8730 0030-8730}, url={http://dx.doi.org/10.2140/pjm.1972.41.57}, DOI={10.2140/pjm.1972.41.57}, number={1}, journal={Pacific Journal of Mathematics}, publisher={Mathematical Sciences Publishers}, author={Campbell, Stephen}, year={1972}, month={Apr}, pages={57–62} }
 @article{campbell_1972, title={The exponential representation of operator valued, differentiable inner functions}, volume={12}, ISSN={0022-0396}, url={http://dx.doi.org/10.1016/0022-0396(72)90018-6}, DOI={10.1016/0022-0396(72)90018-6}, number={3}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Campbell, Stephen L}, year={1972}, month={Nov}, pages={455–461} }