Optimal Control of Switched Systems via Nonlinear Optimization Based on Direct Di erentiations of Value Functions

This paper presents an approach for solving optimal control problems of switched systems. In general, in such problems one needs to nd both optimal continuous inputs and optimal switching sequences, since the system dynamics vary before and after every switching instant. After formulating the optimal control problem, we propose a two stage optimization methodology for it. Since many practical problems only concern Stage 1 optimization where the number of switchings and the sequence of active subsystems are given, we then concentrate on Stage 1 optimization problems and propose a method for solving them, which is via nonlinear optimization and based on direct di erentiations of value functions. Moreover, the method is modi ed and applied to general switched linear quadratic (GSLQ) problems. Implementation diÆculties of the method can be successfully addressed for GSLQ problems. Examples are shown to illustrate the results in the paper.