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Cannarsa, P.; Frankowska, H.
Systems & control letters, 09/2013, Letnik: 62, Številka: 9Journal Article
It is well-known that the value function V of a Bolza optimal control problem fails to be everywhere differentiable. In this paper, however, we show that, if V is proximally subdifferentiable at (t,x), then it is smooth on a neighborhood of (t,x). Our result yields that V stays smooth on a neighborhood of any optimal trajectory starting at a point where the proximal subdifferential is nonempty. This leads to sufficient conditions for the regularity of optimal trajectories and optimal controls.
