Design of robust‐optimal controllers with low trajectory sensitivity for uncertain Takagi–Sugeno fuzzy model systems using differential evolution algorithm

SUMMARY By integrating the robust stabilizability condition, the orthogonal-function approach (OFA) and the Taguchi-sliding-based differential evolution algorithm (TSBDEA), an integrative computational approach is presented in this paper to design the robust-optimal fuzzy parallel-distributed-compensation (PDC) controller with low trajectory sensitivity such that (i) the Takagi–Sugeno (TS) fuzzy model system with parametric uncertainties can be robustly stabilized, and (ii) a quadratic finite-horizon integral performance index for the nominal TS fuzzy model system can be minimized. In this paper, the robust stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the OFA, an algebraic algorithm only involving the algebraic computation is derived for solving the nominal TS fuzzy feedback dynamic equations. By using the OFA and the LMI-based robust stabilizability condition, the robust-optimal fuzzy PDC control problem for the uncertain TS fuzzy dynamic systems is transformed into a static constrained-optimization problem represented by the algebraic equations with constraint of LMI-based robust stabilizability condition; thus, greatly simplifying the robust-optimal PDC control design problem. Then, for the static constrained-optimization problem, the TSBDEA has been employed to find the robust-optimal PDC controllers with low trajectory sensitivity of the uncertain TS fuzzy model systems. A design example is given to demonstrate the applicability of the proposed new integrative approach. Copyright © 2011 John Wiley & Sons, Ltd.