Guaranteed-cost fuzzy filter design for a class of nonlinear discrete-time uncertain systems

In general, it is a difficult work to design an efficient filter for nonlinear systems. This paper studies fuzzy filtering design for nonlinear discrete-time systems. First, the Takagi and Sugeno fuzzy model is proposed to approximate a nonlinear discrete-time system. Next, based on the fuzzy model, the fuzzy estimation for nonlinear discrete-time systems is studied. Using a suboptimal approach, the minimum variance fuzzy estimation problems are characterized in terms of an eigenvalue problem (EVP) by minimizing the upper bound on the variance of the estimation error. The EVP can be solved very efficiently using convex optimization techniques.

[1]  Bor-Sen Chen,et al.  H∞ fuzzy estimation for a class of nonlinear discrete-time dynamic systems , 2001, IEEE Trans. Signal Process..

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

[3]  J. Buckley Sugeno type controllers are universal controllers , 1993 .

[4]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[5]  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..

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

[7]  Lihua Xie,et al.  Robust Kalman filtering for uncertain discrete-time systems , 1994, IEEE Trans. Autom. Control..

[8]  P. Khargonekar,et al.  Robust stabilization of linear systems with norm-bounded time-varying uncertainty , 1988 .

[9]  Bor-Sen Chen,et al.  Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model , 2001, IEEE Trans. Fuzzy Syst..

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

[11]  C. Zheng,et al.  ; 0 ; , 1951 .

[12]  Dennis S. Bernstein,et al.  Robust, reduced-order, nonstrictly proper state estimation via the optimal projection equations with Petersen-Hollot bounds , 1987 .

[13]  Uri Shaked,et al.  Robust discrete-time minimum-variance filtering , 1996, IEEE Trans. Signal Process..

[14]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..