Sampled-data fuzzy controller for continuous nonlinear systems

The sampled-data fuzzy control of nonlinear systems is presented. The consequents of the fuzzy controller rules are linear sampled-data sub-controllers. As a result, the fuzzy controller is a weighted sum of some linear sampled-data sub-controllers that can be implemented by a microcontroller or a digital computer to lower the implementation cost. Consequently, a hybrid fuzzy controller consisting of continuous-time grades of memberships and discrete-time sub-controller is obtained. The system stability of the fuzzy control system is investigated on the basis of Lyapunov-based approach. The sampling activity introduces discontinuity to complicate the system dynamics and make the stability analysis difficult. The proposed fuzzy controller exhibits a favourable property to alleviate the conservativeness of the stability analysis. Furthermore, linear matrix inequality-based performance conditions are derived to guarantee the system performance of the fuzzy control system. An application example is given to illustrate the merits of the proposed approach.

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

[2]  M. Sugeno,et al.  Structure identification of fuzzy model , 1988 .

[3]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[4]  Chieh-Li Chen,et al.  Analysis and design of fuzzy control system , 1993 .

[5]  Vladimir A. Yakubovich,et al.  Linear Matrix Inequalities in System and Control Theory (S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan) , 1995, SIAM Rev..

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

[7]  Kazuo Tanaka,et al.  Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs , 1998, IEEE Trans. Fuzzy Syst..

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

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

[10]  Zengqi Sun,et al.  Analysis and design of fuzzy reduced-dimensional observer and fuzzy functional observer , 2001, Fuzzy Sets Syst..

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

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

[13]  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).

[14]  Akira Ichikawa,et al.  Hinfinity control for sampled-data nonlinear systems described by Takagi-Sugeno fuzzy systems , 2004, Fuzzy Sets Syst..

[15]  Emilia Fridman,et al.  Robust sampled-data stabilization of linear systems: an input delay approach , 2004, Autom..

[16]  Zhou Luan-jie,et al.  Delay-Dependent Robust Stabilization of Uncertain State-Delayed Systems , 2004 .

[17]  Hak-Keung Lam,et al.  Sampled-Data Fuzzy Controller for Time-Delay Nonlinear Systems: Fuzzy-Model-Based LMI Approach , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).