Guaranteed cost control for constrained Takagi-Sugeno fuzzy systems

Abstract Abstract This paper presents a novel control design technique in order to obtain a Guaranteed Cost Fuzzy Controller subject to constraints on the input channel. This Guaranteed cost control law is obtained via multi-parametric Quadratic Programming. The result is a piecewise fuzzy control law where the state partition is defined by fuzzy inequalities. The parameters of the Lyapunov function can be obtained previously using linear matrix inequalities optimization.

[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]  Alberto Bemporad,et al.  An algorithm for multi-parametric quadratic programming and explicit MPC solutions , 2003, Autom..

[3]  Wilfrid Perruquetti,et al.  Non-quadratic stabilisation of discrete Takagi Sugeno fuzzy models , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).

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

[5]  Xiaodong Liu,et al.  Approaches to quadratic stability conditions and H∞ control designs for T-S fuzzy systems , 2003, IEEE Trans. Fuzzy Syst..

[6]  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..

[7]  Gang Feng,et al.  Robust Output Feedback Control of Constrained Nonlinear Processes via Piecewise Fuzzy Anti-Windup Dynamic Compensator , 2007, 2007 American Control Conference.

[8]  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.

[9]  M. Morari,et al.  Geometric Algorithm for Multiparametric Linear Programming , 2003 .

[10]  Alberto Bemporad,et al.  The explicit linear quadratic regulator for constrained systems , 2003, Autom..

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

[12]  Zongli Lin,et al.  Robust stability analysis and fuzzy-scheduling control for nonlinear systems subject to actuator saturation , 2003, IEEE Trans. Fuzzy Syst..