Infinite Horizon Optimal Control of Non-Convex Problems under State Constraints

International audienceWe consider the undiscounted infinite horizon optimal control problem under state constraints in the absence of convexity/concavity assumptions. Then the value function is, in general, nonsmooth. Using the tools of set-valued and nonsmooth analysis, the necessary optimality conditions and sensitivity relations are derived in such a framework. We also investigate relaxation theorems and uniqueness of solutions of the Hamilton-Jacobi-Bellman equation arising in this setting