Feedback in state constrained optimal control

Clarke, Francis H.; Rifford, Ludovic; Stern, R. J.

ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 97-133.

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.

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