On the smoothness of the value function for affine optimal control problems

Davide Barilari (1) , Boarotto Francesco (2)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We prove that the value function associated with an affine optimal control problem with quadratic cost plus a potential is smooth on an open and dense subset of the interior of its attainable set. The result is obtained by a careful analysis of points of continuity of the value function, without assuming any condition on singular minimizers.

Domaines: Optimisation et contrôle [math.OC]; Géométrie différentielle [math.DG]

Davide Barilari, Boarotto Francesco. On the smoothness of the value function for affine optimal control problems . 2016. ⟨hal-01387085⟩