# 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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Journal articles

https://hal.inria.fr/hal-00851753
Contributor : Helene Frankowska <>
Submitted on : Sunday, August 18, 2013 - 9:17:20 AM
Last modification on : Friday, April 10, 2020 - 5:18:03 PM

### 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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