Semiconcavity results and sensitivity relations for the sub-Riemannian distance
Résumé
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]
Origine : Fichiers produits par l'(les) auteur(s)
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