Shifted-Chebyshev-series solution of the Takagi Sugeno fuzzy model based systems

The shifted Chebyshev series approach is developed in this paper to solve the Takagi-Sugeno (TS) fuzzy-model-based dynamic equations. The new method simplifies the procedure of solving the TS-fuzzy-model based dynamic equations into the successive solution of a system of recursive formulae only involving matrix algebra. Based on the presented recursive formulae, an algorithm only involving straightforward algebraic computation is also proposed in this paper. The computational complexity can therefore be reduced remarkably. An illustrated example shows that the proposed method based on the shifted Chebyshev series can obtain satisfactory results

[1]  Ing-Rong Horng,et al.  Shifted Chebyshev series analysis of linear optimal control systems incorporating observers , 1985 .

[2]  Ing-Rong Horng,et al.  Optimal Control of Deterministic Systems Described by Integrodifferential Equations Via Chebyshev Series , 1987 .

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

[4]  Hussein Jaddu,et al.  Direct solution of nonlinear optimal control problems using quasilinearization and Chebyshev polynomials , 2002, J. Frankl. Inst..

[5]  Hussein Jaddu,et al.  Spectral method for constrained linear-quadratic optimal control , 2002, Math. Comput. Simul..

[6]  Mehmet Sezer,et al.  Chebyshev polynomial solutions of systems of high-order linear differential equations with variable coefficients , 2003, Appl. Math. Comput..

[7]  Stephen Barnett,et al.  Matrix Methods for Engineers and Scientists , 1982 .

[8]  Amit Patra,et al.  General Hybrid Orthogonal Functions and their Applications in Systems and Control , 1996 .

[9]  Valder Steffen,et al.  Using Orthogonal Functions for Identification and Sensitivity Analysis of Mechanical Systems , 2002 .

[10]  Elsayed M. E. Elbarbary,et al.  Chebyshev finite difference approximation for the boundary value problems , 2003, Appl. Math. Comput..

[11]  Mark L. Nagurka,et al.  A Chebyshev-based state representation for linear quadratic optimal control , 1993 .

[12]  State estimation using continuous orthogonal functions , 1986 .

[13]  J. Chou Application of Legendre series to the optimal control of integrodifferential equations , 1987 .