Feedback in state constrained optimal control

An optimal control problem is studied, in which the state is required to remain in a compact set S. A control feedback law is constructed which, for given epsilon > 0, produces epsilon-optimal trajectories that satisfy the state constraint universally with respect to all initial conditions in S. The construction relies upon a constraint removal technique which utilizes geometric properties of inner approximations of S and a related trajectory tracking result. The control feedback is shown to possess a robustness property with respect to state measurement error.