Shifted-Chebyshev series solutions of Takagi-Sugeno fuzzy-model-based dynamic equations

By the 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 paper. 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 the straightforward algebraic computation is also proposed in this paper. The computational complexity can, therefore, be reduced remarkably. The illustrated example shows that the proposed method based on the shifted-Chebyshev series can obtain the satisfactory results.