@article{tang_carrette_cai_williamson_daoutidis_2023, title={Automatic decomposition of large-scale industrial processes for distributed MPC on the Shell-Yokogawa Platform for Advanced Control and Estimation (PACE)}, volume={178}, ISSN={["1873-4375"]}, url={https://doi.org/10.1016/j.compchemeng.2023.108382}, DOI={10.1016/j.compchemeng.2023.108382}, abstractNote={The kernel of industrial advanced process control (APC) lies in the formulation and solution of model predictive control (MPC) problems, which specify the controller moves according to the solution of an optimal control problem at each sampling time. A significant challenge is the online computation for large-scale industrial systems. As the state-of-the-art APC technology, the Shell–Yokogawa Platform for Advanced Control and Estimation (PACE) has adopted a systematic framework of handling dynamic optimization of large-scale systems, where an automatic decomposition procedure generates subsystems for distributed MPC. The decomposition is implemented on network representations of the MPC models that capture interactions among process variables, with community detection used to maximize the statistical significance of the subnetworks with preferred internal interconnections. This paper introduces the fundamentals of such a decomposition approach and this functionality in PACE, followed by a case study on a crude distillation process to showcase its industrial application.}, journal={COMPUTERS & CHEMICAL ENGINEERING}, author={Tang, Wentao and Carrette, Pierre and Cai, Yongsong and Williamson, John M. and Daoutidis, Prodromos}, year={2023}, month={Oct} }
 @article{tang_2023, title={Data-Driven State Observation for Nonlinear Systems based on Online Learning}, url={https://doi.org/10.22541/au.168368974.45377787/v1}, DOI={10.22541/au.168368974.45377787/v1}, abstractNote={This paper considers the problem of state observation for nonlinear
dynamics. While model-based observer synthesis is difficult due to the
need of solving partial differential equations, this work proposes an
efficient model-free, data-driven approach based on online learning.
Specifically, by considering the observer dynamics as a Chen-Fliess
series, the estimation of its coefficients has a least squares
formulation. Since the series converges only locally, the coefficients
are recursively updated, resulting in an online optimization scheme
driven by instantaneous gradients. When the state trajectories are
available, the online least squares guarantees an ultimate upper bound
of average observation error proportional to the average variation of
states. In the realistic situations where the states cannot be measured,
the immersed linear dynamics based on the Kazantzis-Kravaris/Luenberger
structure is assigned, followed by online kernel principal component
analysis for dimensionality reduction. The proposed approach is
demonstrated by a limit cycle dynamics and a chaotic system.}, author={Tang, Wentao}, year={2023}, month={May} }
 @article{tang_2023, title={Data-driven state observation for nonlinear systems based on online learning}, volume={8}, ISSN={["1547-5905"]}, url={https://doi.org/10.1002/aic.18224}, DOI={10.1002/aic.18224}, abstractNote={Abstract}, journal={AICHE JOURNAL}, author={Tang, Wentao}, year={2023}, month={Aug} }
 @article{tang_daoutidis_2023, title={Optimal Design of Control-Lyapunov Functions by Semi-Infinite Stochastic Programming}, ISSN={["2576-2370"]}, DOI={10.1109/CDC49753.2023.1038499}, journal={2023 62ND IEEE CONFERENCE ON DECISION AND CONTROL, CDC}, author={Tang, Wentao and Daoutidis, Prodromos}, year={2023}, pages={7277–7284} }
 @article{tang_allman_mitrai_daoutidis_2023, title={Resolving large-scale control and optimization through network structure analysis and decomposition: A tutorial review}, ISSN={["2378-5861"]}, DOI={10.23919/ACC55779.2023.10156560}, abstractNote={Decomposition is a fundamental principle of resolving complexity by scale, which is utilized in a variety of decomposition-based algorithms for control and optimization. In this paper, we aim to give a tutorial review of the following aspects: (i) how to decompose a network representing a control or optimization problem according to its latent block structure, (ii) how decomposition is determined for distributed control, and (iii) how optimization problems are solved under decomposition. Directions for further developing decomposition methods and decomposition-based control and optimization algorithms are also discussed.}, journal={2023 AMERICAN CONTROL CONFERENCE, ACC}, author={Tang, Wentao and Allman, Andrew and Mitrai, Ilias and Daoutidis, Prodromos}, year={2023}, pages={3113–3129} }
 @article{daoutidis_megan_tang_2023, title={The future of control of process systems}, volume={178}, ISSN={["1873-4375"]}, DOI={10.1016/j.compchemeng.2023.108365}, abstractNote={This paper provides a perspective on the major challenges and directions in academic process control research over the next 5–10 years, and its industrial implementation. Large-scale systems control and identification, nonlinear model-based and model-free control, and controller performance monitoring and diagnosis are discussed as major directions for future research, along with control technology and industry workforce challenges and opportunities.}, journal={COMPUTERS & CHEMICAL ENGINEERING}, author={Daoutidis, Prodromos and Megan, Larry and Tang, Wentao}, year={2023}, month={Oct} }
 @article{tang_daoutidis_2021, title={Coordinating distributed MPC efficiently on a plantwide scale: The Lyapunov envelope algorithm}, volume={155}, ISSN={0098-1354}, url={http://dx.doi.org/10.1016/j.compchemeng.2021.107532}, DOI={10.1016/j.compchemeng.2021.107532}, abstractNote={The model predictive control (MPC) of large-scale systems should adopt a distributed optimization approach, where controllers for the constituent subsystems optimize their control actions and iterations are used to coordinate their decisions. The real-time implementation of MPC, however, usually allows very limited time for computation and inevitably needs to be terminated early. In this work, we propose a splitting algorithm for distributed optimization analogous to forward-backward splitting (FBS), where ℓ1 and quadratic penalties are imposed on the violation of interconnecting relations among the subsystems. By designing the involved parameters based on dissipative analysis, the iterations result in the monotonic decrease of a plant-wide Lyapunov function, which we call Lyapunov envelope, thus maintaining closed-loop stability under distributed MPC despite early termination and yielding improving control performance as the allowed computational time or number of iterations increases. The proposed Lyapunov envelope algorithm is tested on an industrial-scale vinyl acetate monomer process.}, journal={Computers & Chemical Engineering}, publisher={Elsevier BV}, author={Tang, Wentao and Daoutidis, Prodromos}, year={2021}, month={Dec}, pages={107532} }
 @article{tang_daoutidis_2021, title={Dissipativity learning control (DLC): Theoretical foundations of input–output data-driven model-free control}, volume={147}, ISSN={0167-6911}, url={http://dx.doi.org/10.1016/j.sysconle.2020.104831}, DOI={10.1016/j.sysconle.2020.104831}, abstractNote={Data-driven, model-free control strategies leverage statistical or learning techniques to design controllers based on data instead of dynamic models. We have previously introduced the dissipativity learning control (DLC) method, where the dissipativity property is learned from the input–output trajectories of a system, based on which L2-optimal P/PI/PID controller synthesis is performed. In this work, we analyze the statistical conditions on dissipativity learning that enable control performance guarantees, and establish theoretical results on performance under nominal conditions as well as in the presence of statistical errors. The implementation of DLC is further formalized and is illustrated on a two-phase chemical reactor, along with a comparison to model identification-based LQG control.}, journal={Systems & Control Letters}, publisher={Elsevier BV}, author={Tang, Wentao and Daoutidis, Prodromos}, year={2021}, month={Jan}, pages={104831} }
 @article{tang_daoutidis_2021, title={Fast and stable nonconvex constrained distributed optimization: the ELLADA algorithm}, volume={23}, ISSN={1389-4420 1573-2924}, url={http://dx.doi.org/10.1007/s11081-020-09585-w}, DOI={10.1007/s11081-020-09585-w}, abstractNote={Distributed optimization using multiple computing agents in a localized and coordinated manner is a promising approach for solving large-scale optimization problems, e.g., those arising in model predictive control (MPC) of large-scale plants. However, a distributed optimization algorithm that is computationally efficient, globally convergent, amenable to nonconvex constraints remains an open problem. In this paper, we combine three important modifications to the classical alternating direction method of multipliers for distributed optimization. Specifically, (1) an extra-layer architecture is adopted to accommodate nonconvexity and handle inequality constraints, (2) equality-constrained nonlinear programming (NLP) problems are allowed to be solved approximately, and (3) a modified Anderson acceleration is employed for reducing the number of iterations. Theoretical convergence of the proposed algorithm, named ELLADA, is established and its numerical performance is demonstrated on a large-scale NLP benchmark problem. Its application to distributed nonlinear MPC is also described and illustrated through a benchmark process system.}, number={1}, journal={Optimization and Engineering}, publisher={Springer Science and Business Media LLC}, author={Tang, Wentao and Daoutidis, Prodromos}, year={2021}, month={Jan}, pages={259–301} }
 @article{tang_daoutidis_2021, title={Nonlinear state and parameter estimation using derivative information: A Lie-Sobolev approach}, volume={151}, ISSN={0098-1354}, url={http://dx.doi.org/10.1016/j.compchemeng.2021.107369}, DOI={10.1016/j.compchemeng.2021.107369}, abstractNote={The implementation of nonlinear control depends on the accuracy of the system model, which, however, is often restricted by parametric and structural uncertainty in the underlying dynamics. In this paper, we propose methods of estimating parameters and states that aim at matching the identified model and the true dynamics not only in the direct output measurements, i.e., in an L2-sense, but also in the higher-order time derivatives of the output signals, i.e., in a Sobolev sense. A Lie-Sobolev gradient descent-based observer-estimator and a Lie-Sobolev moving horizon estimator (MHE) are formulated, and their convergence properties and effects on input–output linearizing control and model predictive control (MPC) respectively are studied. Advantages of Lie-Sobolev state and parameter estimation in nonlinear processes are demonstrated by numerical examples and a reactor with complex dynamics.}, journal={Computers & Chemical Engineering}, publisher={Elsevier BV}, author={Tang, Wentao and Daoutidis, Prodromos}, year={2021}, month={Aug}, pages={107369} }
 @article{mitrai_tang_daoutidis_2021, title={Stochastic blockmodeling for learning the structure of optimization problems}, volume={68}, ISSN={0001-1541 1547-5905}, url={http://dx.doi.org/10.1002/aic.17415}, DOI={10.1002/aic.17415}, abstractNote={Abstract}, number={6}, journal={AIChE Journal}, publisher={Wiley}, author={Mitrai, Ilias and Tang, Wentao and Daoutidis, Prodromos}, year={2021}, month={Sep} }
 @article{tang_daoutidis_2019, title={A Bilevel Programming Approach to the Convergence Analysis of Control-Lyapunov Functions}, volume={64}, ISSN={0018-9286 1558-2523 2334-3303}, url={http://dx.doi.org/10.1109/TAC.2019.2892386}, DOI={10.1109/TAC.2019.2892386}, abstractNote={This paper deals with the estimation of convergence rate and domain of attraction of control-Lyapunov functions in Lyapunov-based control. This pair of estimation problems has been considered only for input-affine systems with constraints on the input norm. In this paper, we propose a novel optimization framework to address the estimation of convergence rate and domain of attraction. Specifically, we formulate the estimation problems as min–max bilevel programs for the decay rate of the Lyapunov function, where the inner problem can be resolved using Karush–Kuhn–Tucker optimality conditions, and the resulting single-level programs can be transformed into and solved as mixed-integer nonlinear programs. The proposed approach is applicable to systems with input-nonaffinity or more general forms of input constraints under an input-convexity assumption.}, number={10}, journal={IEEE Transactions on Automatic Control}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Tang, Wentao and Daoutidis, Prodromos}, year={2019}, month={Oct}, pages={4174–4179} }
 @article{allman_tang_daoutidis_2019, title={DeCODe: a community-based algorithm for generating high-quality decompositions of optimization problems}, volume={20}, ISSN={1389-4420 1573-2924}, url={http://dx.doi.org/10.1007/s11081-019-09450-5}, DOI={10.1007/s11081-019-09450-5}, number={4}, journal={Optimization and Engineering}, publisher={Springer Science and Business Media LLC}, author={Allman, Andrew and Tang, Wentao and Daoutidis, Prodromos}, year={2019}, month={Jun}, pages={1067–1084} }
 @article{daoutidis_tang_allman_2019, title={Decomposition of control and optimization problems by network structure: Concepts, methods, and inspirations from biology}, volume={65}, ISSN={0001-1541 1547-5905}, url={http://dx.doi.org/10.1002/aic.16708}, DOI={10.1002/aic.16708}, abstractNote={AIChE JournalVolume 65, Issue 10 e16708 PERSPECTIVE Decomposition of control and optimization problems by network structure: Concepts, methods, and inspirations from biology Prodromos Daoutidis, Corresponding Author Prodromos Daoutidis daout001@umn.edu Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota Correspondence Prodromos Daoutidis, Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455. Email: daout001@umn.eduSearch for more papers by this authorWentao Tang, Wentao Tang Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MinnesotaSearch for more papers by this authorAndrew Allman, Andrew Allman Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MinnesotaSearch for more papers by this author Prodromos Daoutidis, Corresponding Author Prodromos Daoutidis daout001@umn.edu Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota Correspondence Prodromos Daoutidis, Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455. Email: daout001@umn.eduSearch for more papers by this authorWentao Tang, Wentao Tang Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MinnesotaSearch for more papers by this authorAndrew Allman, Andrew Allman Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MinnesotaSearch for more papers by this author First published: 27 June 2019 https://doi.org/10.1002/aic.16708Citations: 14 Funding information: University of Minnesota; National Science Foundation Read the full textAboutPDF 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 Citing Literature Volume65, Issue10October 2019e16708 RelatedInformation}, number={10}, journal={AIChE Journal}, publisher={Wiley}, author={Daoutidis, Prodromos and Tang, Wentao and Allman, Andrew}, year={2019}, month={Jul} }
 @article{tang_daoutidis_2019, title={Dissipativity learning control (DLC): A framework of input–output data-driven control}, volume={130}, ISSN={0098-1354}, url={http://dx.doi.org/10.1016/j.compchemeng.2019.106576}, DOI={10.1016/j.compchemeng.2019.106576}, abstractNote={The paper addresses data-driven control based on input–output data in the absence of an underlying dynamic model. It proposes a dissipativity learning control (DLC) framework which involves the data-based learning of the dissipativity property of the control system, followed by a dissipativity-based controller design procedure. Specifically, independent component analysis and parametric distribution inference are adopted to estimate a polyhedral region of input–output trajectory samples, whose dual cone characterizes the dissipativity property; subsequently, an optimal controller in the L2 sense is designed by solving a nonlinear semidefinite programming problem. The applicability of the proposed method is demonstrated by case studies on regulating control of a polymerization reactor and tracking control of an oscillatory chemical reactor.}, journal={Computers & Chemical Engineering}, publisher={Elsevier BV}, author={Tang, Wentao and Daoutidis, Prodromos}, year={2019}, month={Nov}, pages={106576} }
 @article{tang_daoutidis_2019, title={Distributed control and optimization of process system networks: A review and perspective}, volume={27}, ISSN={1004-9541}, url={http://dx.doi.org/10.1016/j.cjche.2018.08.027}, DOI={10.1016/j.cjche.2018.08.027}, abstractNote={Large-scale and complex process systems are essentially interconnected networks. The automated operation of such process networks requires the solution of control and optimization problems in a distributed manner. In this approach, the network is decomposed into several subsystems, each of which is under the supervision of a corresponding computing agent (controller, optimizer). The agents coordinate their control and optimization decisions based on information communication among them. In recent years, algorithms and methods for distributed control and optimization are undergoing rapid development. In this paper, we provide a comprehensive, up-to-date review with perspectives and discussions on possible future directions.}, number={7}, journal={Chinese Journal of Chemical Engineering}, publisher={Elsevier BV}, author={Tang, Wentao and Daoutidis, Prodromos}, year={2019}, month={Jul}, pages={1461–1473} }
 @article{daoutidis_allman_khatib_moharir_palys_pourkargar_tang_2019, title={Distributed decision making for intensified process systems}, volume={25}, ISSN={2211-3398}, url={http://dx.doi.org/10.1016/j.coche.2018.12.007}, DOI={10.1016/j.coche.2018.12.007}, abstractNote={Process intensification can afford considerable benefits with respect to economics, sustainability and/or safety but also presents increased decision making challenges with respect to computational efficiency and flexibility across multiple temporal and spatial scales. Distributed decision making, that is, localized yet coordinated decision making among constituent subsystems, is a promising approach to alleviating these challenges. Determination of these subsystems is at the heart of the distributed paradigm. This paper gives a summary of recent developments and future directions in distributed decision making for intensified systems, specifically with respect to optimization, control and monitoring, with emphasis on methods for obtaining high quality decompositions for such problems based on network theory. It also discusses integrated renewable energy and chemical production, a new and promising domain of large-scale process intensification, in the context of systems engineering challenges and opportunities.}, journal={Current Opinion in Chemical Engineering}, publisher={Elsevier BV}, author={Daoutidis, Prodromos and Allman, Andrew and Khatib, Shaaz and Moharir, Manjiri A and Palys, Matthew J and Pourkargar, Davood Babaei and Tang, Wentao}, year={2019}, month={Sep}, pages={75–81} }
 @article{constantino_tang_daoutidis_2019, title={Topology Effects on Sparse Control of Complex Networks with Laplacian Dynamics}, volume={9}, ISSN={2045-2322}, url={http://dx.doi.org/10.1038/s41598-019-45476-6}, DOI={10.1038/s41598-019-45476-6}, abstractNote={Abstract}, number={1}, journal={Scientific Reports}, publisher={Springer Science and Business Media LLC}, author={Constantino, Pedro H. and Tang, Wentao and Daoutidis, Prodromos}, year={2019}, month={Jun} }
 @article{daoutidis_tang_jogwar_2018, title={Decomposing complex plants for distributed control: Perspectives from network theory}, volume={114}, ISSN={0098-1354}, url={http://dx.doi.org/10.1016/j.compchemeng.2017.10.015}, DOI={10.1016/j.compchemeng.2017.10.015}, abstractNote={This paper reviews recent research on the application of methods from the theory of networks for developing distributed control architectures for complex plants. The problem is defined as one of decomposing process networks into constituent subnetworks with strong intra-subnetwork and weak inter-subnetwork interactions. These interactions are quantified based on connectivity and response sensitivity information. This perspective is inspired by the community detection problem in networks. Several approaches are discussed based on hierarchical clustering and modularity optimization. The concepts and potential of these methods for developing control architectures for complex plants are illustrated through a case study. Future research directions are also discussed.}, journal={Computers & Chemical Engineering}, publisher={Elsevier BV}, author={Daoutidis, Prodromos and Tang, Wentao and Jogwar, Sujit S.}, year={2018}, month={Jun}, pages={43–51} }
 @article{tang_daoutidis_2018, title={Distributed adaptive dynamic programming for data-driven optimal control}, volume={120}, ISSN={0167-6911}, url={http://dx.doi.org/10.1016/j.sysconle.2018.08.002}, DOI={10.1016/j.sysconle.2018.08.002}, abstractNote={Adaptive dynamic programming (ADP), as an important optimal control technique, can be exploited in the setting of data-driven control based on an approximate regression-based solution of the Hamilton–Jacobi–Bellman (HJB) equations. Distributed optimization algorithms, which are extensively studied in statistics and machine learning, have not yet been applied to the solution of data-driven ADP problems. In this work, we identify the data-driven ADP problem as a consensus optimization problem for nonlinear affine systems, and apply the alternating direction method of multipliers (ADMM) and its accelerated variants for its solution. For the input-constrained optimal control problem, we define a combined optimal primal–dual function to develop a data-based version of the input-constrained HJB equation.}, journal={Systems & Control Letters}, publisher={Elsevier BV}, author={Tang, Wentao and Daoutidis, Prodromos}, year={2018}, month={Oct}, pages={36–43} }
 @article{tang_daoutidis_2018, title={Network decomposition for distributed control through community detection in input–output bipartite graphs}, volume={64}, ISSN={0959-1524}, url={http://dx.doi.org/10.1016/j.jprocont.2018.01.009}, DOI={10.1016/j.jprocont.2018.01.009}, abstractNote={This paper addresses the decomposition of network systems for distributed control. We construct a novel weighted input–output bipartite graph representation of control systems, in which the input–output edge weights capture topological connectivity and short-time response sensitivities. We then introduce community detection as a network-theoretic tool to generate a decomposition with strong intra-subsystem interactions and weak inter-subsystem interactions. A modularity-based graph bisection procedure is applied recursively to determine the optimal decomposition. The proposed method is applied to a chemical process network example.}, journal={Journal of Process Control}, publisher={Elsevier BV}, author={Tang, Wentao and Daoutidis, Prodromos}, year={2018}, month={Apr}, pages={7–14} }
 @article{tang_allman_pourkargar_daoutidis_2018, title={Optimal decomposition for distributed optimization in nonlinear model predictive control through community detection}, volume={111}, ISSN={0098-1354}, url={http://dx.doi.org/10.1016/j.compchemeng.2017.12.010}, DOI={10.1016/j.compchemeng.2017.12.010}, abstractNote={Distributed optimization, based on a decomposition of the entire optimization problem, has been applied to many complex decision making problems in process systems engineering, including nonlinear model predictive control. While decomposition techniques have been widely adopted, it remains an open problem how to optimally decompose an optimization problem into a distributed structure. In this work, we propose to use community detection in network representations of optimization problems as a systematic method of partitioning the optimization variables into groups, such that the variables in the same groups generally share more constraints than variables between different groups. The proposed method is applied to the decomposition of the optimal control problem involved in the nonlinear model predictive control of a reactor-separator process, and the quality of the resulting decomposition is examined by the resulting control performance and computational time. Our result suggests that community detection in network representations of the optimization problem generates decompositions with improvements in computational performance as well as a good optimality of the solution.}, journal={Computers & Chemical Engineering}, publisher={Elsevier BV}, author={Tang, Wentao and Allman, Andrew and Pourkargar, Davood Babaei and Daoutidis, Prodromos}, year={2018}, month={Mar}, pages={43–54} }
 @article{tang_babaei pourkargar_daoutidis_2018, title={Relative time‐averaged gain array (RTAGA) for distributed control‐oriented network decomposition}, volume={64}, ISSN={0001-1541 1547-5905}, url={http://dx.doi.org/10.1002/aic.16130}, DOI={10.1002/aic.16130}, abstractNote={Input‐output partitioning for decentralized control has been studied extensively using various methods, including those based on relative gains and those based on relative degrees and sensitivities. These two concepts are characterizations of long‐time and short‐time input‐output response, respectively. A unifying new input‐output interaction measure, called relative time‐averaged gain, which characterizes the input‐output interactions during a time scale of interest for linear time‐invariant systems is proposed. This measure is used as a basis for community detection in the input‐output bipartite graph of a process network to produce subnetworks whose responses are weakly coupled in the time scale of interest. As such, the resulting decomposition accounts for both response characteristics and the network topology, and can be used efficiently for distributed control architecture design. In a case study, the proposed decomposition is applied to the distributed model predictive control of a reactor‐separator benchmark process. © 2018 American Institute of Chemical Engineers AIChE J, 64: 1682–1690, 2018}, number={5}, journal={AIChE Journal}, publisher={Wiley}, author={Tang, Wentao and Babaei Pourkargar, Davood and Daoutidis, Prodromos}, year={2018}, month={Feb}, pages={1682–1690} }
 @article{kang_tang_liu_daoutidis_2016, title={Control configuration synthesis using agglomerative hierarchical clustering: A graph-theoretic approach}, volume={46}, ISSN={0959-1524}, url={http://dx.doi.org/10.1016/j.jprocont.2016.07.009}, DOI={10.1016/j.jprocont.2016.07.009}, abstractNote={Abstract This paper addresses the synthesis of control configurations that have optimal structural coupling characteristics between manipulated inputs and controlled outputs in terms of relative degrees. A recently developed agglomerative hierarchical clustering approach is reformulated in a graph theoretic setting. This allows the efficient generation of decentralized control configuration as well as the entire hierarchy of block decentralized control configurations. In addition, a notion of modularity is used to evaluate the compactness and separation of the resulting clusters, allowing the identification of optimal control configurations. The application of the proposed method is illustrated through case studies on an energy integrated fuel-cell system and a heat exchanger network.}, journal={Journal of Process Control}, publisher={Elsevier BV}, author={Kang, Lixia and Tang, Wentao and Liu, Yongzhong and Daoutidis, Prodromos}, year={2016}, month={Oct}, pages={43–54} }