Abstract
This paper studies some regularity properties of the minimum time functionT for a nonlinear control system with a general targetK. Under a Petrov type controllability assumption,T is shown to be semiconcave if the distance fromK is semiconcave. A semiconvexity result also holds for linear control systems with convex targets. These properties are then applied to study the structure of the set of nondifferentiability points ofT.
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Partially supported by the Italian National Project MURST 40% “Problemi nonlineari...”.