Robust H2 fuzzy output feedback control for discrete-time nonlinear systems with parametric uncertainties

This paper deals with the robust H"2 fuzzy observer-based control problem for discrete-time uncertain nonlinear systems. The Takagi and Sugeno (T-S) fuzzy model is employed to represent a discrete-time nonlinear system with parametric uncertainties. A fuzzy observer is used to estimate the state of the fuzzy system and a non-parallel distributed compensation (non-PDC) scheme is adopted for the control design. A fuzzy Lyapunov function (FLF) is constructed to derive a sufficient condition such that the closed-loop fuzzy system is globally asymptotically stable and an upper bound on the quadratic cost function is provided. A sufficient condition for the existence of a robust H"2 fuzzy observer-based controller is presented in terms of linear matrix inequalities (LMIs). Moreover, by using the existing LMI optimization techniques, a suboptimal fuzzy observer-based controller in the sense of minimizing the cost bound is proposed. Finally, an example is given to illustrate the effectiveness of the proposed design method.

[1]  Kazuo Tanaka,et al.  Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H∞ control theory, and linear matrix inequalities , 1996, IEEE Trans. Fuzzy Syst..

[2]  H. O. Wang,et al.  Multiobjective control of a vehicle with triple trailers , 2002 .

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

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

[5]  G. Feng,et al.  Quadratic stabilization of uncertain discrete-time fuzzy dynamic systems , 2001 .

[6]  Yong-Yan Cao,et al.  Robust H∞ disturbance attenuation for a class of uncertain discrete-time fuzzy systems , 2000, IEEE Trans. Fuzzy Syst..

[7]  Kazuo Tanaka,et al.  Corrections To "robust Stabilization Of A Class Of Uncertain Nonlinear Systems Via Fuzzy Control: Quadratic Stabilizability, H Control Theory, And Linear Matrix Inequalities" [Correspondence] , 1997, IEEE Trans. Fuzzy Syst..

[8]  Xi Li,et al.  Delay-dependent robust H control of uncertain linear state-delayed systems , 1999, Autom..

[9]  Kazuo Tanaka,et al.  An approach to fuzzy control of nonlinear systems: stability and design issues , 1996, IEEE Trans. Fuzzy Syst..

[10]  A. Jadbabaie,et al.  Guaranteed-cost design of continuous-time Takagi-Sugeno fuzzy controllers via linear matrix inequalities , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[11]  Bor-Sen Chen,et al.  Mixed H2/H∞ fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach , 2000, IEEE Trans. Fuzzy Syst..

[12]  Gang Feng,et al.  H infinity Control of nonlinear discrete-time systems based on dynamical fuzzy models , 2000, Int. J. Syst. Sci..

[13]  Shengyuan Xu,et al.  Robust Hinfinite control for discrete-time fuzzy systems via basis-dependent Lyapunov functions , 2005, Inf. Sci..

[14]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[15]  Gang Feng,et al.  H∞ control of uncertain dynamical fuzzy discrete-time systems , 2001, IEEE Trans. Syst. Man Cybern. Part B.

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

[17]  Bor-Sen Chen,et al.  Mixed Fuzzy Output Feedback Control Design for Nonlinear Dynamic Systems: An LMI Approach , 2000 .

[18]  Kai-Yuan Cai,et al.  H2 guaranteed cost fuzzy control design for discrete-time nonlinear systems with parameter uncertainty , 2006, Autom..

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

[20]  Jin Bae Park,et al.  Robust fuzzy control of nonlinear systems with parametric uncertainties , 2001, IEEE Trans. Fuzzy Syst..

[21]  Shaocheng Tong,et al.  Observer-based robust fuzzy control of nonlinear systems with parametric uncertainties , 2002, Fuzzy Sets Syst..

[22]  Yung-Sheng Liu,et al.  A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems , 2003, SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483).

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

[24]  H. C. Pietrobom,et al.  On relaxed LMI-based designs for fuzzy regulators and fuzzy observers , 2001, ECC.

[25]  Huijun Gao,et al.  Improved Hinfinite control of discrete-time fuzzy systems: a cone complementarity linearization approach , 2005, Inf. Sci..

[26]  Xin-Ping Guan,et al.  Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays , 2004, IEEE Transactions on Fuzzy Systems.

[27]  Kai-Yuan Cai,et al.  H2 guaranteed cost fuzzy control for uncertain nonlinear systems via linear matrix inequalities , 2004, Fuzzy Sets Syst..

[28]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[29]  Sérgio Ricardo de Souza,et al.  ℋ2 guaranteed cost control for uncertain discrete-time linear systems , 1993 .

[30]  Euntai Kim,et al.  New approaches to relaxed quadratic stability condition of fuzzy control systems , 2000, IEEE Trans. Fuzzy Syst..

[31]  Toshimitsu Ushio,et al.  Chaotic synchronization and controlling chaos based on contraction mappings , 1995 .

[32]  Ian R. Petersen,et al.  Optimal guaranteed cost control of discrete‐time uncertain linear systems , 1998 .

[33]  Ji-Chang Lo,et al.  Observer-based robust H/sub /spl infin// control for fuzzy systems using two-step procedure , 2004, IEEE Transactions on Fuzzy Systems.

[34]  Pierre Apkarian,et al.  Parameterized linear matrix inequality techniques in fuzzy control system design , 2001, IEEE Trans. Fuzzy Syst..

[35]  Jong Hae Kim,et al.  Output feedback robust H∞ control of uncertain fuzzy dynamic systems with time-varying delay , 2000, IEEE Trans. Fuzzy Syst..