Optimal controller design of time-varying TS-fuzzy-model-based systems via Chebyshev series and genetic algorithm

A direct computational algorithm, by using the elegant operational properties of the shifted Chebyshev series (SCS), for solving the time-varying Takagi-Sugeno (TS) fuzzy-model-based feedback dynamic equations is first developed in this paper. The developed computational algorithm only involves the straightforward algebraic computation. Then, the developed algorithm is integrated with the hybrid Taguchi-genetic algorithm (HTGA) to design the optimal non-parallel-distributed-compensation (non-PDC) controller (linear state feedback controller) of the time-varying TS-fuzzy-model-based control systems under the criterion of minimizing a quadratic integral performance index, where the integral performance index is also converted into the algebraic form by using the SCS approach (SCSA). Thus, this proposed approach facilitates the design task of the non-PDC optimal controller for the time-varying TS-fuzzy-model-based control systems. A design example of the optimal non-PDC controller for the pendulum system with the vibration in the vertical direction on the pivot point is given to demonstrate the applicability of the proposed approach.