Local regularity of the value function in optimal control - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Systems and Control Letters Year : 2013

Local regularity of the value function in optimal control

Piermarco Cannarsa
  • Function : Author
  • PersonId : 859188
Hélène Frankowska
  • Function : Author
  • PersonId : 899311

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.

Dates and versions

hal-00851753 , version 1 (18-08-2013)

Identifiers

Cite

Piermarco Cannarsa, Hélène Frankowska. Local regularity of the value function in optimal control. Systems and Control Letters, 2013, 62, pp.791--794. ⟨10.1016/j.sysconle.2013.06.001⟩. ⟨hal-00851753⟩
146 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More