Design of Stable and Quadratic Optimal Linear State Feedback Controllers for TS-Fuzzy-Model-Based Control Systems

This paper considers the stable and quadratic finite-horizon optimal design problem of the linear state feedback controllers for the Takagi-Sugeno (TS) fuzzy-model-based control systems by integrating the stabilizability condition, the shifted-Chebyshev-series approach (SCSA), and the hybrid Taguchi-genetic algorithm (HTGA), where the stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the SCSA, an algorithm only involving the algebraic computation is derived in this paper for solving the TS-fuzzy-model-based feedback dynamic equations, and then is integrated with both the proposed sufficient LMI condition and the HTGA to design the stable and quadratic optimal linear state feedback controllers of the TS-fuzzy-model-based control systems under the criterion of minimizing a quadratic integral performance index, where the quadratic integral performance index is also converted into the algebraic form by using the SCSA. The presented new approach, which integrates the proposed LMI-based stabilizability condition, the SCSA and the HTGA, is non-differential, non-integral, straightforward, and well-adapted to computer implementation. The computational complexity may therefore be reduced remarkably. Thus, this proposed approach facilitates the design task of the stable and quadratic optimal linear state feedback controllers for the TS-fuzzy-model-based control systems. A design example of stable and quadratic optimal linear state feedback controller for the ball-and-beam system is given to demonstrate the applicability of the proposed new integrative approach