Adaptive Fuzzy Inverse Optimal Control of Nonlinear Switched Systems

Existing approaches to optimal control of 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 not only the cost function but also 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.