Semiconcavity of the value function for exit time problems with nonsmooth target

Carlo Sinestrari

doi:10.3934/cpaa.2004.3.757

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2004, Volume 3, Issue 4: 757-774. Doi: 10.3934/cpaa.2004.3.757

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Semiconcavity of the value function for exit time problems with nonsmooth target

Carlo Sinestrari^1,

1.
Dipartimento di Matematica, Università di Roma, Via della Ricerca Scientifica 1, 00133 Roma

Received: November 30, 2003

Revised: April 30, 2004

Published: November 2004

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Abstract

We prove semiconcavity of the value function of a nonlinear optimal control problem where the cost functional depends on the arrival time of the trajectory on a given target set. We make suitable smoothness assumptions on the dynamics of the system, while the target set can be completely general. As a corollary, we prove differentiability of the value function for a class of linear systems.

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Mathematics Subject Classification: 49L25, 35D10, 49L20.

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Semiconcavity of the value function for exit time problems with nonsmooth target

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