Set separation, approximating multicones, and the Lipschitz maximum principle

[摘要] 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. (C) 2007 Published by Elsevier Inc.

[发布日期] 2007-12-15

[关键词] Pontryagin Maximum Principle;set separation;transversality;Lipschitz