https://hal-univ-avignon.archives-ouvertes.fr/hal-03644131Bayen, TérenceTérenceBayenLMA - EA2151 Laboratoire de Mathématiques d'Avignon - AU - Avignon UniversitéBouali, AnasAnasBoualiLMA - EA2151 Laboratoire de Mathématiques d'Avignon - AU - Avignon UniversitéBourdin, LoïcLoïcBourdinXLIM-MATHIS - Mathématiques & Sécurité de l'information - XLIM - XLIM - UNILIM - Université de Limoges - CNRS - Centre National de la Recherche ScientifiqueOptimal control problems with non-control regions: necessary optimality conditionsHAL CCSD2022Optimal controlnon-control regionsPontryagin maximum principle[MATH] Mathematics [math][MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Bouali, Anas2022-04-18 19:37:092023-03-24 14:53:262022-04-20 11:53:20enConference papersapplication/pdf1We consider a smooth control system that is subject to loss of control in the sense that the state space is partitioned into several disjoint regions and, in each region, either the system can be controlled, as usual, in a permanent way (that is, one can change the value of the control at any real time), or, on the contrary, the control has to remain constant from the entry time into the region until the exit time. The latter case corresponds to a non-control region. The objective of this paper is to state the necessary optimality conditions for a Mayer optimal control problem in such a setting of loss of control. Our main result is based on a hybrid maximum principle that takes into account a regionally switching parameter.