@article{zhu_wu_karimi_lu_2019, title={Special issue on advanced analysis and control design of switching linear parameter-varying systems and its applications}, volume={233}, ISSN={["2041-3041"]}, DOI={10.1177/0959651818819594}, abstractNote={As the linear parameter-varying (LPV) system has a large range of parameter variations, it is very difficult to achieve satisfactory control performance for the whole range of parameter variation merely through a constant controller. An effective approach to ensure the desired control performance is to divide the whole parameter range into some sub-ranges, and each sub-range corresponds to a controller. The desired performance can be satisfied via the switching of controllers belonging to different sub-ranges. Accordingly, the LPV control issues involved with certain switching properties (e.g. nondeterministic or stochastic) have received increasing interests within recent decades, and a quite large number of useful results have been reported assuming the switching signals with nondeterministic (e.g. average dwell time (ADT), persistent dwell time) or Markov stochastic properties. However, about some applications in practice, various non-ideal situations might occur, for instance, the exact values of scheduling parameters may not be valid to adapt to controller parameters owing to sensor drift and noise; the system states are not measurable completely for the desired controllers/filters in that a full knowledge of the state vector is rarely available; the various complex dynamics such as model uncertainty, time delays, and faults often exist in the practical systems, all of which bring new challenges and opportunities for theoretical researchers and applied practitioners alike. In terms of the above discussion on motivations, eight papers are chosen in this special issue from a large number of submissions via a normative peer-review process. These collections contain both theoretical and application-oriented studies for showcasing emerging innovative ideas and technologies, to address various unresolved issues and challenges in the field of hybrid LPV control systems. The main contributions of these studies are briefly provided as follows. First, considering the switched LPV systems with nondeterministic switching properties in the continuous-time domain, Zhao et al. investigate the issue of HN fault-tolerant control for a class of continuous-time switched LPV systems with actuator failures by the multiple discretized parameterdependent Lyapunov functions approach. The proposed Lyapunov technique avoids the Zeno behavior produced by the parameter and state-dependent switching approach. A new switching strategy is established depending on the parameter, state, and dwelltime (DT), which eliminates the assumption on the finite number of switching for any finite time. An application to a turbofan engine is illustrated to verify the utility of the obtained results. Next, Ren et al. address the input–output finite-time stability and finite-time boundedness for a class of continuous-time switched LPV systems with ADT switching based on an eventtriggered communication scheme. An asynchronous switching strategy is considered when deriving the sufficient conditions of stability and boundedness in finite time, and the design of parameter-dependent asynchronous controllers is performed by resolving a group of linear matrix inequalities. The effectiveness of the proposed methods is demonstrated via a numerical example. Furthermore, Ren et al. discuss the finite-time non-fragile full-order controller design issue for a class of continuous-time switched LPV systems based on the multiple Lyapunov function approach. Finally, under the ADT switching, Wang et al. study the HN filter design problem for a class of continuous-time switched LPV systems with both time-varying state and parameter delays. An improved reciprocally convex inequality is used to deal with the terms of delays, and the multiple Lyapunov function method is employed to derive the stability condition with less conservatism, which ensures the existence of novel parameterdependent filters with a guaranteed HN performance. Turning to the field of switched LPV systems with Markov stochastic switching properties, Shen et al. deal with the passive gain-scheduling filtering problem for a class of discrete-time Markov jump LPV systems in the presence of random occurring fading channels. The description of mode information between the system and the presented filter is made via a hidden Markov model. The sufficient conditions are obtained to ensure the existence of an available passive gain-scheduling filter with the aid of the stochastic analysis theory. Besides, Wang et al. concern with the issue of stochastic finite-time HN filtering issue for a class of continuous-}, number={1}, journal={PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART I-JOURNAL OF SYSTEMS AND CONTROL ENGINEERING}, author={Zhu, Yanzheng and Wu, Fen and Karimi, Hamid Reza and Lu, Bei}, year={2019}, month={Jan}, pages={3–4} }
 @article{lu_choi_buckner_tammi_2008, title={Linear parameter-varying techniques for control of a magnetic bearing system}, volume={16}, ISSN={["1873-6939"]}, DOI={10.1016/j.conengprac.2008.01.002}, abstractNote={In this paper, a linear parameter-varying (LPV) control design method is evaluated experimentally on an active magnetic bearing (AMB) system. A speed-dependent LPV model of the AMB system is derived. Model uncertainties are identified using artificial neural networks, and an uncertainty weighting function is approximated for LPV control synthesis. Experiments are conducted to verify the robustness of LPV controllers for a wide range of rotational speed. This LPV control approach eliminates the need for gain-scheduling, and provides better performance than the traditional proportional-integral-derivative control for high-speed operation.}, number={10}, journal={CONTROL ENGINEERING PRACTICE}, author={Lu, Bei and Choi, Heeju and Buckner, Gregory D. and Tammi, Kari}, year={2008}, month={Oct}, pages={1161–1172} }
 @article{lu_wu_2006, title={Probabilistic robust linear parameter-varying control of an F-16 aircraft}, volume={29}, ISSN={["1533-3884"]}, DOI={10.2514/1.22495}, abstractNote={O PERATIONAL capability at high angles of attack, especially near and at post stall regimes, is critical for next generation fighter aircrafts and uninhabited aerial vehicles [1]. However, significantly large levels of modeling uncertainty are inevitably encountered inflight control design for those regimes. The sources of uncertainty include variations in mass, inertia, and center of gravity positions, uncertainty in the aerodynamic data, etc. [2]. The maneuverability at high angles of attack poses a challenging control problem that requires guaranteeing both robust stability and robust performance in the presence of large parameter variations. Traditional robust control techniques, like H1 and -synthesis, have been proven to be capable of producing robust uncertaintytolerant controllers for next generation aircrafts [2,3]. However, those techniques focus on deterministic worst-case robust analysis and synthesis, which often lead to overly conservative stability bound estimate and high control effort. Moreover, a large number of conventional deterministic problems in robustness analysis and synthesis are shown to be NP-hard. To reduce conservatism and computational complexity, one approach is to shift the meaning of robustness from its usual deterministic sense to a probabilistic one [4]. In contrast to traditional robust control techniques, only a probabilistic solution is given, and a certain risk-level should be accepted. However, such a system may be viewed as being practically robust from an engineering point of view. Algorithms derived in the probabilistic context are based on uncertainty randomization and usually called randomized algorithms, which may be divided into two families: methods based on statistical learning theory [5], and sequential methods based on subgradient iterations [6–8] or ellipsoid iterations [9,10]. The former can deal with nonconvex synthesis problems; however, it resorts to randomized search over the controller parameters to find a candidate solution. On the other hand, the sequential methods are formulated based on convex problems, thus avoiding the controller randomization issue [4]. The probabilistic robust control approach is still in the stage of algorithm development and improvement, and has not been explored in depth for flight control. The number of implementation of probabilistic techniques is therefore rather restricted. In the late 90s, Marrison and Stengel designed a linear quadratic regulator to control the nonlinear longitudinal dynamics of a hypersonic aircraft [11]. Recently, Wang and Stengel designed a robust flight control system for the high-incidence research model problem by combining stochastic robustness with nonlinear dynamic inversion [12]. Their work was based on statistical learning theory, and controllers were searched by using generic algorithms to minimize stochastic robustness cost functions. In our earlier paper, we applied an ellipsoid algorithm to design anH1 controller for a linearized F-16 longitudinal model [13]. Good stability and performance robustness have been achieved at the chosen flight condition. The motivation for this research is twofold. First, the probabilistic control design method for linear time-invariant plants in [13] is generalized to linear parameter-varying (LPV) systems. This generalization is very important because of the relevance of LPV systems to nonlinear systems. TheLPVcontrol synthesis condition is known to be formulated as a convex problemwith a set of parameterdependent linear matrix inequalities (LMIs) [14–16]. Second, the current state of the art does not allow accurate aerodynamicmodeling in the high angle of attack region. Because of its random nature, uncertainty in the aerodynamic data can be characterized using a statistical model, which can be handled effectively by the promising probabilistic robust control approach. Note that the study in this note focuses on the robustness issue with respect to the aerodynamic uncertainty at high angles of attack, and the results would be easily generalized to other parametric uncertainties, such as variations in mass and inertial properties. Because of the convex formulation of LPV control synthesis, the sequential method is more suitable for dealing with uncertainties and designing probabilistic robust LPV controllers. An ellipsoid algorithm with a stopping rule proposed by Oishi [10] is used to determine feasible solutions to LMI synthesis conditions. The paper is organized as follows. In Sec. II, the ellipsoid algorithm is presented, which either gives a probabilistic solution with high confidence or detects that there is no deterministic solution in an approximated sense. Section III first provides a brief overview of robust control problem of an uncertain LPV system, and then discusses the computational issues when the algorithm is applied to the robust LPV control problem. In Sec. IV, a robust LPV controller is designed for an F-16 aircraft with large aerodynamic uncertainty, and the robust performance is tested through nonlinear simulations. Finally, the paper concludes with a summary in Sec. V.}, number={6}, journal={JOURNAL OF GUIDANCE CONTROL AND DYNAMICS}, author={Lu, Bei and Wu, Fen}, year={2006}, pages={1454–1460} }
 @article{lu_wu_kim_2005, title={Linear parameter-varying antiwindup compensation for enhanced flight control performance}, volume={28}, ISSN={["1533-3884"]}, DOI={10.2514/1.4952}, abstractNote={Actuator saturation is one of the major issues of flight control in the high angle-of-attack region. This paper presents a saturation control scheme for linear parameter varyjing (LPV) systems from an antiwindup control perspective. The proposed control approach is advantageous from the implementation standpoint because it can be thought of as an augmented control algorithm to the existing control system. Moreover, the synthesis condition for an antiwindup compensator is formulated as a linear matrix inequality (LMI) optimization problem and can be solved efficiently. We have applied te LPV antiwindup controller to an F-16 longitudinal autopilot control system design and compared it with the thrust vectoring control scheme. The nonlinear simulations show that an LPV antiwindup controller improves flight quality and offers advantages over thrust vectoring in a high angle-of-attack region.}, number={3}, journal={JOURNAL OF GUIDANCE CONTROL AND DYNAMICS}, author={Lu, B and Wu, F and Kim, SW}, year={2005}, pages={494–505} }
 @article{wu_lu_2004, title={Anti-windup control design for exponentially unstable LTI systems with actuator saturation}, volume={52}, ISSN={["1872-7956"]}, DOI={10.1016/j.sysconle.2004.02.007}, abstractNote={In this paper, a new saturation control technique in the framework of anti-windup compensation is developed for exponentially unstable linear time-invariant systems subject to input nonlinearities. The proposed control algorithm guarantees regional stability in the existence of input saturation, and provides less conservative performance than most existing anti-windup schemes. Moreover, an explicit form of anti-windup controller with its order no more than the order of the plant is derived. An inverted pendulum example is used to demonstrate the advantages of the newly proposed anti-windup control technique.}, number={3-4}, journal={SYSTEMS & CONTROL LETTERS}, author={Wu, F and Lu, B}, year={2004}, month={Jul}, pages={305–322} }
 @article{wu_bei_2004, title={On convexified robust control synthesis}, volume={40}, ISSN={["1873-2836"]}, DOI={10.1016/j.automatica.2004.01.010}, abstractNote={In this paper, we study a convexified robust control problem and its relation to gain-scheduling control. It reveals that the robust control synthesis condition becomes convex under a special plant structure. Moreover, for this class of robust control problems, the gain-scheduling control approach from scaled small-gain theorem will not provide any performance improvement over convexified robust controllers. Based on this observation, a convexified robust control synthesis framework with stringent performance and computational efficacy is proposed.}, number={6}, journal={AUTOMATICA}, author={Wu, F and Bei, L}, year={2004}, month={Jun}, pages={1003–1010} }
 @article{lu_wu_2004, title={Switching LPV control designs using multiple parameter-dependent Lyapunov functions}, volume={40}, ISSN={0005-1098}, url={http://dx.doi.org/10.1016/j.automatica.2004.06.011}, DOI={10.1016/j.automatica.2004.06.011}, abstractNote={In this paper we study the switching control of linear parameter-varying (LPV) systems using multiple parameter-dependent Lyapunov functions to improve performance and enhance control design flexibility. A family of LPV controllers is designed, each suitable for a specific parameter subregion. They are switched so that the closed-loop system remains stable and its performance is optimized. Two switching logics, hysteresis switching and switching with average dwell time, are examined. The control synthesis conditions for both switching logics are formulated as matrix optimization problems, which are generally non-convex but can be convexified under some simplifying assumptions. The hysteresis switching LPV control scheme is then applied to an active magnetic bearing problem.}, number={11}, journal={Automatica}, publisher={Elsevier BV}, author={Lu, Bei and Wu, Fen}, year={2004}, month={Nov}, pages={1973–1980} }