Simultaneous Design of Parallel Distributed Output Feedback and Anti-windup Compensators for Constrained Takagi-Sugeno Fuzzy Systems

This paper is devoted to developing a novel approach to deal with constrained continuous-time nonlinear systems in the form of Takagi-Sugeno fuzzy models. Here, the disturbed systems are subject to both input and state constraints. The one-step design method is used to simultaneously synthesize the dynamic output feedback controller and its anti-windup strategy. A parameter-dependent version of the generalized sector condition is used together with Lyapunov stability theory to derive linear matrix inequality design conditions. Based on this result and for different design specifications, the synthesis of an anti-windup based dynamic output feedback controller is expressed on the form of convex optimization problems. A physically motivated example is given to illustrate the effectiveness of the proposed method.

[1]  Hak-Keung Lam,et al.  Stable and robust fuzzy control for uncertain nonlinear systems , 2000, IEEE Trans. Syst. Man Cybern. Part A.

[2]  Frank L. Lewis,et al.  Computational intelligence in control , 2014, Annu. Rev. Control..

[3]  Gérard Scorletti,et al.  Control of rational systems using linear-fractional representations and linear matrix inequalities , 1996, Autom..

[4]  Sophie Tarbouriech,et al.  Anti-windup design with guaranteed regions of stability for discrete-time linear systems , 2004, Proceedings of the 2004 American Control Conference.

[5]  Kenji Sawada,et al.  Generalized sector synthesis of output feedback control with anti-windup structure , 2009, Syst. Control. Lett..

[6]  Youxian Sun,et al.  Online SVM regression algorithm-based adaptive inverse control , 2007, Neurocomputing.

[7]  Yong-Nong Chang,et al.  Robust anti-windup controller design of time-delay fuzzy systems with actuator saturations , 2011, Inf. Sci..

[8]  G. Feng,et al.  A Survey on Analysis and Design of Model-Based Fuzzy Control Systems , 2006, IEEE Transactions on Fuzzy Systems.

[9]  Michel Dambrine,et al.  Lyapunov-based robust control design for a class of switching non-linear systems subject to input saturation: application to engine control , 2014 .

[10]  Kazuo Tanaka,et al.  Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach , 2008 .

[11]  Sophie Tarbouriech,et al.  Stability and Stabilization of Linear Systems with Saturating Actuators , 2011 .

[12]  M. Sami Fadali,et al.  On the Stability and Control of Continuous-Time TSK Fuzzy Systems , 2013, IEEE Transactions on Cybernetics.

[13]  Kevin Guelton,et al.  Non-quadratic local stabilization for continuous-time Takagi-Sugeno models , 2012, Fuzzy Sets Syst..

[14]  Gang Feng,et al.  Robust Model Predictive Control for Discrete-Time Takagi–Sugeno Fuzzy Systems With Structured Uncertainties and Persistent Disturbances , 2014, IEEE Transactions on Fuzzy Systems.

[15]  Haiping Du,et al.  Fuzzy Control for Nonlinear Uncertain Electrohydraulic Active Suspensions With Input Constraint , 2009, IEEE Trans. Fuzzy Syst..

[16]  Marius-Lucian Tomescu,et al.  Fuzzy Logic Control System Stability Analysis Based on Lyapunov's Direct Method , 2009, Int. J. Comput. Commun. Control.

[17]  Mayuresh V. Kothare,et al.  Simultaneous linear and anti-windup controller synthesis using multiobjective convex optimization , 2009, Autom..

[18]  Thierry-Marie Guerra,et al.  LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form , 2004, Autom..

[19]  Víctor C. S. Campos,et al.  Revisiting the TP Model Transformation: Interpolation and Rule Reduction , 2015 .

[20]  Jian Xiao,et al.  Static Output Feedback Control for Interval Type‐2 T‐S Fuzzy Systems Based on Fuzzy Lyapunov Functions , 2014 .

[21]  Jiaqi Huang,et al.  High-order tracking differentiator based adaptive neural control of a flexible air-breathing hypersonic vehicle subject to actuators constraints. , 2015, ISA transactions.

[22]  Shengwei Wang,et al.  Application of two‐loop robust control to air‐conditioning systems , 2009 .

[23]  Chen-Sheng Ting,et al.  A Robust Fuzzy Control Approach to Stabilization of Nonlinear Time-delay Systems with Saturating Inputs , 2008 .

[24]  Huaping Liu,et al.  Piecewise Fuzzy Anti-Windup Dynamic Output Feedback Control of Nonlinear Processes With Amplitude and Rate Actuator Saturations , 2009, IEEE Trans. Fuzzy Syst..

[25]  Chun-Hsiung Fang,et al.  Robust H∞ fuzzy static output feedback control of T-S fuzzy systems with parametric uncertainties , 2007, Fuzzy Sets Syst..

[26]  J Boada,et al.  Multi-saturation anti-windup structure for satellite control , 2010, Proceedings of the 2010 American Control Conference.

[27]  Manfred Morari,et al.  A unified framework for the study of anti-windup designs , 1994, Autom..

[28]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[29]  Johan A. K. Suykens,et al.  Support Vector Machines: A Nonlinear Modelling and Control Perspective , 2001, Eur. J. Control.

[30]  Tong-heng Lee,et al.  Technical communique: Improvement on observer-based H∞ control for T-S fuzzy systems , 2005 .

[31]  Kazuo Tanaka,et al.  A multiple Lyapunov function approach to stabilization of fuzzy control systems , 2003, IEEE Trans. Fuzzy Syst..

[32]  L. Xiaodong,et al.  New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI , 2003, Autom..

[33]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[34]  Antoine Dequidt,et al.  Anti-windup based dynamic output feedback controller design with performance consideration for constrained Takagi-Sugeno systems , 2015, Eng. Appl. Artif. Intell..

[35]  Luca Zaccarian,et al.  Output feedback design for saturated linear plants using deadzone loops , 2009, Autom..

[36]  Antonio Sala,et al.  Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya's theorem , 2007, Fuzzy Sets Syst..

[37]  Baocang Ding.  Quadratic boundedness via dynamic output feedback for constrained nonlinear systems in Takagi-Sugeno's form , 2009, Autom..