The Viability Kernel Algorithm for Computing Value Functions of Infinite Horizon Optimal Control Problems

We characterize in this paper the epigraph of the value function of a discounted infinite horizon optimal control problem as the viability kernel of an auxiliary differential inclusion. Then the viability kernel algorithm applied to this problem provides the value function of the discretized optimal control problem as the supremum of a nondecreasing sequence of functions iteratively defined. We also use the fact that an upper Painlev´e]Kuratowski limit of closed viability domains is a viability domain to prove the convergence of the discrete value functions