Optimal control problems with non-control regions: necessary optimality conditions

Térence Bayen (1) , Anas Bouali (1) , Loïc Bourdin (2)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon
2 XLIM-MATHIS - Mathématiques & Sécurité de l'information

We 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.

Keywords: Optimal control; non-control regions; Pontryagin maximum principle

Domains: Mathematics [math]; Optimization and Control [math.OC]

Térence Bayen, Anas Bouali, Loïc Bourdin. Optimal control problems with non-control regions: necessary optimality conditions. 18th IFAC workshop on control applications of optimization, Jul 2022, Gif-sur-Yvette, France. ⟨hal-03644131⟩