The Role of Metric Regularity in State Constrained Optimal Control

The aim of this paper is to show that a common set of analytical tools (conditions for metric regularity of the state constraint) resolve a number of important questions in state constrained optimal control. On the one hand, they lead to simple, directly verifiable criteria for non-degeneracy of the state constrained Maximum Principle. On the other hand, they make possible the characterization of the value function as a unique solution to the Hamilton-Jacobi equation, in an appropriate generalized sense, for problems with state and endpoint constraints.