Design of Stable and Quadratic-optimal Static Output Feedback Controllers for Ts-fuzzy-model-based Control Systems: an Integrative Computational Approach

By integrating the stabilizability condition, the orthogonal-functions approach (OFA) and the hybrid Taguchi-genetic algorithm (HTGA), an integrative computational method is presented in this paper to design the stable and quadratic-optimal static output feedback parallel-distributed-compensation (PDC) controller such that (i) the TakagiSugeno (TS) fuzzy-model-based control system can be stabilized, and (ii) a quadratic finite-horizon integral performance index for the TS-fuzzy-model-based control system can be minimized. In this paper, the stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). By using the OFA and the LMI-based stabilizability condition, the stable and quadratic-finite-horizon-optimal static output feedback PDC control problem for the TS-fuzzy-model-based dynamic systems is transformed into a static constrained-optimization problem represented by the algebraic equations with constraint of LMI-based stabilizability condition, thus greatly simplifying the optimal static output feedback PDC control design problem. Then, for the static constrained-optimization problem, the HTGA is employed to find the stable and quadratic-optimal static output feedback PDC controllers of the TS-fuzzy-model-based control systems. A design example of stable and quadratic-optimal static output feedback PDC controller for a nonlinear inverted pendulum system controlled by a separately excited direct-current (DC) motor is given to demonstrate the applicability of the proposed integrative computational approach.