Existence of neighboring feasible trajectories: Applications to dynamic programming for state-constrained optimal control problems

In this paper, the value function for an optimal control problem with endpo int and state constraints is characterized as the unique lower semicontinuo us generalized solution of the Hamilton-Jacobi equation. This is achieved u nder a constraint qualification (CQ) concerning the interaction of the stat e and dynamic constraints. The novelty of the results reported here is part ly the nature of(CQ) and partly the proof techniques employed, which are ba sed on new estimates of the distance of the set of state trajectories satis fying a state constraint from a given trajectory which violates the constra int.