A Dynamic Programming Approach for Optimal Control of Switched Systems

In optimal control problems of switched systems, in general, one needs to find both optimal continuous inputs and optimal switching sequences, since the system dynamics vary before and after every switching instant. In a previous paper, we proved that an optimal control problem can be posed as a two stage optimization problem under some additional assumptions. In general, the two stage optimization problem is still difficult to solve analytically. In this paper, we develop a search algorithm to explore the solution of the two stage optimization problem and find useful suboptimal solutions. This algorithm is motivated by the idea of dynamic programming which studies the value functions. The algorithm is used to determine suboptimal solutions for general switched linear quadratic problems.