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Convexity properties of the minimum time function

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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...”.

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Cannarsa, P., Sinestrari, C. Convexity properties of the minimum time function. Calc. Var 3, 273–298 (1995). https://doi.org/10.1007/BF01189393

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