Semiconcavity results and sensitivity relations for the sub-Riemannian distance. (July 2019)

• Record Type: Journal Article
• Authors: Basco, Vincenzo; Cannarsa, Piermarco; Frankowska, Hélène
• Is Part Of: Nonlinear analysis. Volume 184(2019)
• Page Start: 298
• Page End: 320
• Publication Date: 2019-07
• Subjects: Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.02.008
• Languages: English
• ISSNs: 0362-546X

Abstract

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 .