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 Gamma subset of R-n. Such a regularity result was obtained by the second author and L. Rifford in Cannarsa and Rifford (2008) when Gamma is a singleton. Furthermore, we derive sensitivity relations for time optimal control problems with general target sets Gamma, that is, without imposing any geometric assumptions on Gamma. (C) 2019 Elsevier Ltd. All rights reserved.
Basco, V., Cannarsa, P., Frankowska, H. (2019). Semiconcavity results and sensitivity relations for the sub-Riemannian distance. NONLINEAR ANALYSIS, 184, 298-320 [10.1016/j.na.2019.02.008].
Semiconcavity results and sensitivity relations for the sub-Riemannian distance
Basco V.;Cannarsa P.
;
2019-01-01
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 Gamma subset of R-n. Such a regularity result was obtained by the second author and L. Rifford in Cannarsa and Rifford (2008) when Gamma is a singleton. Furthermore, we derive sensitivity relations for time optimal control problems with general target sets Gamma, that is, without imposing any geometric assumptions on Gamma. (C) 2019 Elsevier Ltd. All rights reserved.| File | Dimensione | Formato | |
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