Hybridization of optimal control problems

Optimization problems for hybrid systems have attracted a lot of attention in recent years. This interest stimulated numerous scientific works and the development of tools to study optimal trajectories, such as necessary conditions. The idea of the present contribution is to use such results for hybrid systems to construct a hybridization of an optimal control problem. The approximation via a hybrid system was already considered in the literature, but using different methods to obtain a reduction to minimal path problems on a graph. Our procedure gives an efficient approximation, i.e. more efficient than standard discretization.