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 k ernel of an auxiliary differential inclusion. Then the viability kerne l algorithm applied to this problem provides the value function of the discretized optimal control problem as the supremum of a nondecreasin g sequence of functions iteratively defined. We also use the fact that an upper Painleve-Kuratowski limit of closed viability domains is a v iability domain to prove the convergence of the discrete value functio ns. (C) 1996 Academic Press, Inc.