Calculus of Variations and Geometric Measure Theory

D. Barilari - F. Boarotto

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

created by barilari on 21 Oct 2016
modified on 11 Oct 2018


Published Paper

Inserted: 21 oct 2016
Last Updated: 11 oct 2018

Journal: SIAM Journal of Control and Optimization
Year: 2018


We study the regularity properties of the value function associated with an ane optimal control problem with quadratic cost plus a potential, for a fixed fi nal time and initial point. Without assuming any condition on singular minimizers, we prove that the value function is continuous on an open and dense subset of the interior of the attainable set. As a byproduct we obtain that it is actually smooth on a possibly smaller set, still open and dense.