### 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...