Sensitivity relations for the Mayer problem with differential inclusions - Université Paris Cité Accéder directement au contenu
Article Dans Une Revue ESAIM: Control, Optimisation and Calculus of Variations Année : 2015

Sensitivity relations for the Mayer problem with differential inclusions

Résumé

In optimal control, sensitivity relations are usually understood as inclusions that identify the pair formed by the dual arc and the Hamiltonian, evaluated along the associated minimizing trajectory, as a suitable generalized gradient of the value function. In this paper, sensitivity relations are obtained for the Mayer problem associated with the di fferential inclusion and applied to derive optimality conditions. Our first application concerns the maximum principle and consists in showing that a dual arc can be constructed for every element of the superdi fferential of the final cost. As our second application, with every nonzero limiting gradient of the value function at some point (t; x) we associate a family of optimal trajectories at (t; x) with the property that families corresponding to distinct limiting gradients have empty intersection.
Fichier principal
Vignette du fichier
COCV_22-09_2_.pdf (377.05 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00991204 , version 1 (14-05-2014)
hal-00991204 , version 2 (11-08-2014)
hal-00991204 , version 3 (26-09-2014)

Identifiants

Citer

Piermarco Cannarsa, Hélène Frankowska, Teresa Scarinci. Sensitivity relations for the Mayer problem with differential inclusions. ESAIM: Control, Optimisation and Calculus of Variations, 2015, 21 (3), pp.789 - 814. ⟨10.1051/cocv/2014050⟩. ⟨hal-00991204v3⟩
260 Consultations
237 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More