A semi-Lagrangian algorithm in policy space for hybrid optimal control problems

The mathematical framework of hybrid system is a recent and general tool to treat control systems involving control action of heterogeneous nature. In this paper, we construct and test a semi-Lagrangian numerical scheme for solving the Dynamic Programming equation of an infinite horizon optimal control problem for hybrid systems. In order to speed up convergence, we also propose and analyze an acceleration technique based on policy iteration. Finally, we validate the approach via some numerical tests in low dimension.