Semiconcavity results and sensitivity relations for the sub-Riemannian distance. (July 2019) - Basco, Vincenzo; Cannarsa, Piermarco; Frankowska, Hélène
Abstract: Regularity properties are investigated for the value function of the Bolza optimal control problem with affine dynamic and end-point constraints. In the absence of singular geodesics, we prove the local semiconcavity of the sub-Riemannian distance from a compact set Γ ⊂ R n . Such a regularity result was obtained by the second author and L. Rifford in Cannarsa and Rifford (2008) when Γ is a singleton. Furthermore, we derive sensitivity relations for time optimal control problems with general target sets Γ, that is, without imposing any geometric assumptions on Γ .