Semiconcavity results and sensitivity relations for the sub-Riemannian distance

Vincenzo Basco (1, 2) , Piermarco Cannarsa (2) , Hélène Frankowska (3, 1)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 DIPMAT - Dipartimento di Matematica [Roma II]
3 C&O - Equipe combinatoire et optimisation

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 [Semiconcavity results for optimal control problems admitting no singular minimizing controls, Annales de l'IHP Analyse non linéaire 25(4): 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.

Domaines: Mathématiques [math]

Vincenzo Basco, Piermarco Cannarsa, Hélène Frankowska. Semiconcavity results and sensitivity relations for the sub-Riemannian distance. Nonlinear Analysis: Theory, Methods and Applications, 2019, 184, pp.298-320. ⟨10.1016/j.na.2019.02.008⟩. ⟨hal-02126121⟩