Stable and Quadratic Optimal Control for TS Fuzzy-Model-Based Time-Delay Control Systems

For the finite-horizon optimal control problem of the Takagi-Sugeno (TS) fuzzy-model-based time-delay control systems, by integrating the delay-dependent stabilizability condition, the shifted-Chebyshev-series approach (SCSA), and the hybrid Taguchi-genetic algorithm (HTGA), an integrative method is presented to design the stable and quadratic optimal parallel distributed compensation (PDC) controllers. In this paper, the delay-dependent stabilizability 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 paper for solving the TS fuzzy-model-based time-delay feedback dynamic equations. In addition, by using the SCSA, the stable and quadratic optimal PDC control problem for the TS fuzzy-model-based time-delay control systems is replaced by a static parameter optimization problem represented by the algebraic equations with constraint of the LMI-based stabilizability condition, thus greatly simplifying the stable and optimal PDC control design problem. The computational complexity for both differential and integral in the stable and optimal PDC control design of the original dynamic systems may therefore be reduced considerably. Then, for the static constrained optimization problem, the HTGA is employed to find the stable and quadratic optimal PDC controllers of the TS fuzzy-model-based time-delay control systems. A design example of the stable and quadratic optimal PDC controllers for the continuous-stirred-tank-reactor system is given to demonstrate the applicability of the proposed integrative approach.