Semicontinuous Solutions of Hamilton-Jacobi-Bellman Equations with Degenerate State Constraints

Abstract

In this paper, the value function of a Bolza optimal control problem with state constraints is characterized as the unique lower semicontinuous solution of a Hamilton-Jacobi equation. The state constraints are given by an arbitrary closed set with possibly empty interior. In particular, Soner's inward pointing condition is extended here to the case of degenerate state constraints. © 2000 Academic Press.