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.
Sinestrari, C. (2004). Semiconcavity of the value function for exit time problems with nonsmooth target. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 3(4), 757-774 [10.3934/cpaa.2004.3.757].
Semiconcavity of the value function for exit time problems with nonsmooth target
SINESTRARI, CARLO
2004-01-01
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.File in questo prodotto:
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