Introducing shape-dependent relaxed conditions in fuzzy control of nonlinear systems in Takagi-Sugeno form

Most of the fuzzy literature presents stability and performance results in fuzzy control of Takagi-Sugeno models via LMI conditions; such conditions are independent of the particular shape of the LMIs. Shape-dependent conditions may be used to relax the results: some of them are only conditions on the memberships themselves; others include relations between state variables and memberships. The latter approach, then, enters into the realm of actual nonlinear control, departing from the conventional analysis which proves stability of nonlinear systems via proving stability of some linear time-variant convex-hull models (the Takagi-sugeno systems). The conditions may be made polynomial with the sum-of-squares approach. With the ideas in this paper, the gap between fuzzy and nonlinear control gets smaller.

[1]  Miguel Bernal,et al.  A Membership-Function-Dependent Stability Analysis of Takagi-Sugeno Models , 2008 .

[2]  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..

[3]  Kazuo Tanaka,et al.  Stabilization of Polynomial Fuzzy Systems via a Sum of Squares Approach , 2007, 2007 IEEE 22nd International Symposium on Intelligent Control.

[4]  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).

[5]  Antonio Sala,et al.  Relaxed LMI conditions for closed-loop fuzzy systems with tensor-product structure , 2007, Eng. Appl. Artif. Intell..

[6]  Miguel Bernal,et al.  A membership-function-dependent approach for stability analysis and controller synthesis of Takagi-Sugeno models , 2009, Fuzzy Sets Syst..

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

[8]  Antonio Sala,et al.  Relaxed Stability and Performance Conditions for Takagi–Sugeno Fuzzy Systems With Knowledge on Membership Function Overlap , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

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

[11]  Karl-Erik Årzén,et al.  Piecewise quadratic stability of fuzzy systems , 1999, IEEE Trans. Fuzzy Syst..

[12]  H.O. Wang,et al.  A Sum of Squares Approach to Stability Analysis of Polynomial Fuzzy Systems , 2007, 2007 American Control Conference.

[13]  Antonio Sala,et al.  Design of Multiple-Parameterisation PDC Controllers via Relaxed Conditions for Multi-Dimensional Fuzzy Summations , 2007, 2007 IEEE International Fuzzy Systems Conference.

[14]  Antonio Sala,et al.  Reducing the gap between fuzzy and nonlinear control , 2007 .

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

[16]  Hak-Keung Lam,et al.  Stability analysis of fuzzy control systems subject to uncertain grades of membership , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[17]  Antonio Sala,et al.  Extensions to “Stability Analysis of Fuzzy Control Systems Subject to Uncertain Grades of Membership” , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[19]  Antonio Sala,et al.  Relaxed Stability and Performance LMI Conditions for Takagi--Sugeno Fuzzy Systems With Polynomial Constraints on Membership Function Shapes , 2008, IEEE Transactions on Fuzzy Systems.

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

[21]  Robert Babuska,et al.  Perspectives of fuzzy systems and control , 2005, Fuzzy Sets Syst..

[22]  Kazuo Tanaka,et al.  Fuzzy control systems design and analysis , 2001 .

[23]  Antonio Sala,et al.  Is bridging the gap between fuzzy and nonlinear control possible (partially)? , 2007, 2007 European Control Conference (ECC).