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This study proposes a method of designing quadratic optimal fuzzy parallel-distributed-compensation controllers for a class of time-varying Takagi–Sugeno fuzzy model–based time-delay control systems used to solve the finite-horizon optimal control problem. The proposed method fuses the orthogonal function approach and the improved hybrid Taguchi-genetic algorithm. The Taguchi-genetic algorithm only requires algebraic computation to perform the algorithm used to solve time-varying Takagi–Sugeno fuzzy model–based time-delay feedback dynamic equations. The fuzzy parallel-distributed-compensation controller design problem is simplified by using the Taguchi-genetic algorithm to transform the static parameter optimization problem into an algebraic equation. The static optimization problem can then be solved easily by using the improved hybrid Taguchi-genetic algorithm to find the quadratic optimal parallel-distributed-compensation controllers of the time-varying Takagi–Sugeno fuzzy model–based time-delay control systems. The applicability of the proposed integrative method is demonstrated in a real-world design problem.

A shifted Chebyshev series approach for solve the Takagi-Sugeno (TS) fuzzy model based time-delay dynamic equations (TSFMTDE) is developed in this article. The new method simplifies the procedure of solving the TSFMTDE into the solution of a system of recursive formulae involving only matrix algebra. An algorithm based on these recursive formulae, and including only straightforward algebraic computation is also proposed in this article. The new approach proposed is non-iterative, non-differential, non-integral, straightforward, and well-adapted to computer implementation. Two numerical examples are provided. The first shows that the proposed method based on the shifted Chebyshev series may yield close-to-exact solutions. The second (a nonlinear mass-spring-damper mechanical time-delay system with a fuzzy parallel-distributed-compensation controller) demonstrates the application of the proposed approach.

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