Optimal control of uncertain fuzzy model based delay systems

For the finite-horizon optimal control problem of uncertain Takagi-Sugeno (TS) fuzzy-model-based time-delay control systems, by complementarily fusing the orthogonal-functions approach (OFA), the Taguchi-immune algorithm (TIA) and the delay-dependent stabilizability condition, an integrative method is presented to design the stable and quadratic-optimal fuzzy 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 OFA, an algorithm only involving the algebraic computation is derived in this paper for solving the uncertain TS-fuzzy-model-based time-delay feedback dynamic equations. By using the OFA and the LMI-based stabilizability condition, the stable and quadratic-optimal PDC control problem for uncertain TS-fuzzy-model-based time-delay control 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 quadratic 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 TIA can be easily employed to find the stable and quadratic-optimal PDC controllers for uncertain TS-fuzzy-model-based time-delay control systems. The proposed integrative method fusing the OFA, the TIA and the LMI technique can be viewed as one of the hard-computing-assisted soft-computing category, where the OFA and the LMI technique belong to the hard computing constituents and the TIA is one of the soft computing constituents. A design example of the stable and quadratic-optimal PDC controllers for the pendulum time-delay system with the vibration in the vertical direction on the pivot point is given to demonstrate the app- - licability of the proposed new integrative approach.