Strategies for Computing Switching Feedback Controllers

We consider the problem of computing suboptimal feedback switching controllers for discrete dynamical systems. The paper shows how to combine convex optimization techniques with relaxed dynamic programming. We apply the method to several problems that have been considered recently in the literature. A particularly interesting example is given by a DC-DC converter. The proposed algorithm has several interesting properties. The main theoretical result of this paper is the introduction of a new approximate policy iteration algorithm which is shown to converge to the optimal cost function.