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Hsu, M.-R.; Ho, W.-H.; Chou, J.-H.

Numerical solutions of time-varying TS-fuzzy-model-based time-delay dynamic equations via orthogonal functions. (English) Zbl 1127.65040

Int. J. Syst. Sci. 38, No. 5, 377-387 (2007).
Summary: The approach of orthogonal functions to solve the time-varying Takagi-Sugeno (TS) fuzzy-model-based time-delay dynamic equations (time-varying TSFMTDE) is presented [cf. T. Takagi and M. Sugeno, IEEE Trans. Syst. Man Cybern. 15, 116–132 (1985; Zbl 0576.93021)]. The new method simplifies the procedure of solving the time-varying TSFMTDE into the successive solution of a system of recursive formulae only involving matrix algebra. Based on the presented recursive formulae, an algorithm only including straightforward algebraic computation is also proposed in this paper. The new proposed approach is non-iterative, non-differential, non-integral, straightforward, and well-adapted to computer implementation. Hence, the computational complexity is considerably reduced. The first illustrated example shows that the proposed method, based on the orthogonal functions, can obtain satisfactory results. The second illustrated example, for the pendulum time-delay system with the vibration in the vertical direction on the pivot point having a fuzzy parallel-distributed-compensation controller, is given to demonstrate the application of the proposed approach.

MSC:

65K10 Numerical optimization and variational techniques
93C15 Control/observation systems governed by ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
26E50 Fuzzy real analysis

Keywords:

time-varying Takagi-Sugeno fuzzy model; orthogonal functions; numerical examples; time-delay dynamic equations; algorithm; computational complexity; pendulum; vibration

Citations:

Zbl 0576.93021
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Full Text: DOI

References:

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