Analysis of TS-fuzzy-model-based systems via shifted Chebyshev series

By use of the elegant operational properties of the shifted Chebyshev series, a direct computational algorithm for solving the Takagi-Sugeno (TS) fuzzy-model-based dynamic equations is developed In this work. The basic idea is that the state variables are expressed in terms of the shifted Chebyshev series. 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 taking only two terms of expansion coefficients. Based on the presented recursive formulae, an algorithm only involving straightforward algebraic computation is also proposed In this work. The new proposed approach is non-iterative, non-differential, non- integral, straightforward, and well adapted to computer implementation. The computational complexity can therefore be reduced remarkably. The illustrated example shows that the proposed method based on the shifted Chebyshev series can obtain satisfactory results.