Abstract
We present a general necessary condition for separation of the reachable set of a Lipschitz control system from another given set of states, expressed in terms of an “approximating multicone” to the set in a sense that contains as special cases the Clarke and Mordukhovich cones. We then show how this separation result implies a strengthened form of the usual sufficient condition for local controllability along the reference curve and the necessary condition for optimality.
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