Year: 2025
Type: article
Abstract: We consider a general Mayer optimal control problem whose controlled dynamics is defined regionally, and, additionally, we suppose that the interface between two regions is nonsmooth in the sense that it is described by a locally Lipschitz continuous function. Our objective is to derive a hybrid maximum principle in this setting. Doing so, we consider a sequence of mollifiers which allows us to approximate uniformly the interface between two regions by a sequence of smooth functions. This makes possible to apply the hybrid maximum principle on a sequence of approximated optimal control problems involving the smooth interface in place of the nonsmooth one. By passing to the limit as the approximation parameter tends to zero, we obtain the desired necessary optimality conditions in the form of a nonsmooth hybrid maximum principle. Our approach relies on the derivation of subgradients of a locally Lipschitz continuous function via mollifiers.
Source: Journal of convex analysis
DOI: 10.68381/jca32010
Authors: Térence Bayen, Anas Bouali, Florent Nacry
Institutions: Université d'Avignon et des Pays de Vaucluse, Laboratoire de Mathématiques d'Avignon, Université de Montpellier, Institut Agro Montpellier, Institut National de Recherche pour l'Agriculture, l'Alimentation et l'Environnement, Mathématiques, Informatique et Statistique pour l'Environnement et l'Agronomie, Université de Perpignan
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4393026787