Robust Finite-Time Optimal Linear State Feedback Control of Uncertain TS-Fuzzy-Model-Based Control Systems

Abstract

This paper considers the robust quadratic finite-time optimal design problem of the quadratic optimal linear state feedback controllers for the Takagi-Sugeno (TS) fuzzy-model-based control systems with elemental parametric uncertainties by integrating the robust stability condition, the shifted-Chebyshev-series approach (SCSA), and the hybrid Taguchi-genetic algorithm (HTGA), where the robust stability condition takes the elemental information of parametric uncertain matrices into consideration and is proposed in terms of linear matrix inequalities (LMls). Based on the SCSA, an algorithm only involving the algebraic computation is derived in this paper for solving the nominal TS-fuzzy-model-based feedback dynamic equations. By using the SCSA and the LMI-based robust stabilizability condition, the robust quadratic finite-time optimal linear state feedback control problem for the uncertain TS-fuzzy-model-based dynamic systems is transformed into a static constrained-optimization problem represented by algebraic equations with constraint of LMI-based robust stabilizability condition; thus greatly simplifying the robust optimal linear state feedback control design problem. Then, for the static constrained-optimization problem, the HTGA is employed to find the robust quadratic optimal linear state feedback controllers of the uncertain TS-fuzzy-model-based control systems.