Adaptive Fuzzy Inverse Optimal Control of Nonlinear Switched Systems

Abstract

Existing approaches to optimal control for uncertain switched systems require heavy computations for approximating and learning the optimal solution of the Hamilton—Jacobi—Bellman equation. To overcome this problem, a fuzzy adaptive inverse optimal control strategy is first developed for switched systems, which minimizes the cost functional but circumvents solving the Hamilton—Jacobi—Bellman equation. Specifically, an alternative practical inverse approach is developed by two Lyapunov functions method, based on which the inverse optimality regarding a meaningful cost function is achieved. In addition, a new condition of admissible edge-dependent average dwell time is developed by applying the extended multiple Lyapunov functions method. Guided by this weaker condition, the stability of the considered switched system is proved. Finally, simulations are carried out to verify the developed method.