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. (C) 2013 Elsevier B.V. All rights reserved.
Cannarsa, P., Frankowska, H. (2013). Local regularity of the value function in optimal control. SYSTEMS & CONTROL LETTERS, 62(9), 791-794 [10.1016/j.sysconle.2013.06.001].
Local regularity of the value function in optimal control
CANNARSA, PIERMARCO;
2013-01-01
Abstract
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. (C) 2013 Elsevier B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
