Robust-stable and quadratic-optimal control for TS-fuzzy-model-based control systems with elemental parametric uncertainties

By integrating the robust stabilisability condition, the shifted-Chebyshev-series approach (SCSA), and the hybrid Taguchi-genetic algorithm (HTGA), an integrative method is presented in this work to design the robust-stable and quadratic-optimal fuzzy parallel distributed compensation (PDC) controller such that: (i) the Takagi-Sugeno (TS) fuzzy-model-based control system with elemental parametric uncertainties can be robustly stabilised, and (ii) a quadratic finite-horizon integral performance index for the nominal TS-fuzzy-model-based control system can be minimised. In this work, the robust stabilisability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the SCSA, an algebraic algorithm only involving the algebraic computation is derived in this work for solving the nominal TS-fuzzy-model-based feedback dynamic equations. By using the SCSA and the LMI-based robust stabilisability condition, the robust-stable and quadratic-finite-horizon-optimal fuzzy PDC control problem for the uncertain TS-fuzzy-model-based dynamic systems is transformed into a static constrained-optimisation problem represented by the algebraic equations with constraint of LMI-based robust stabilisability condition; thus greatly simplifying the robust optimal PDC control design problem. Then, for the static constrained-optimisation problem, the HTGA is employed to find the robust-stable and quadratic-optimal PDC controllers of the uncertain TS-fuzzy-model-based control systems. A design example of the robust-stable and quadratic-optimal PDC controller for the nonlinear mass-spring-damper mechanical system with elemental parametric uncertainties is given to demonstrate the applicability of the proposed new integrative approach