Global optimal control of perturbed systems

We propose a new numerical method for the computation of the optimal value function of perturbed control systems and associated globally stabilizing optimal feedback controllers. The method is based on a set-oriented discretization of the state space in combination with a new algorithm for the computation of shortest paths in weighted directed hypergraphs. Using the concept of multivalued game, we prove the convergence of the scheme as the discretization parameter goes to zero.