# Local regularity of the value function in optimal control

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.
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Article dans une revue
Systems and Control Letters, Elsevier, 2013, 62, pp.791--794. 〈10.1016/j.sysconle.2013.06.001〉

https://hal.inria.fr/hal-00851753
Contributeur : Helene Frankowska <>
Soumis le : dimanche 18 août 2013 - 09:17:20
Dernière modification le : jeudi 11 janvier 2018 - 06:12:14

### Citation

Piermarco Cannarsa, Hélène Frankowska. Local regularity of the value function in optimal control. Systems and Control Letters, Elsevier, 2013, 62, pp.791--794. 〈10.1016/j.sysconle.2013.06.001〉. 〈hal-00851753〉

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