Optimal Switching and Control of Nonlinear Switching Systems Using Approximate Dynamic Programming

The problem of optimal switching and control of switching systems with nonlinear subsystems is investigated in this paper. An approximate dynamic programming-based algorithm is proposed for learning the optimal cost-to-go function based on the switching instants and the initial conditions. The global optimal switching times for every selected initial condition are directly found through the minimization of the resulting function. Once the optimal switching times are calculated, the same neurocontroller is used to provide optimal control in a feedback form. Proof of convergence of the learning algorithm is presented. Two illustrative numerical examples are given to demonstrate the versatility and accuracy of the proposed technique.