Switched Systems Optimal Control Formulation and a Two Stage Optimization Methodology

|This paper provides an approach toward 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. Since many practical problems only concern Stage 1 optimization where the number of switchings and the order of active subsystems are given, we concentrate on Stage 1 and develop an algorithm based on di erentiations of the value function with respect to the switching instants. The algorithm is also applied to general switched linear quadratic problems and the advantages are discussed. Keywords| Switched Systems, Optimal Control, Nonlinear Optimizations.