19 janvier 2023, 11.00
Salle X 133
A hybrid maximum principle including regional switching parameters.
In this presentation, we consider a Mayer optimal control problem where the controlled system is defined over a partition of the euclidean space, and we assume that the dynamics depends on some additional regionally switching parameter. This means that the parameter should remain constant as long as the trajectory belongs to a given stratum, but, in contrast with optimal control problems including (constant) parameters, it is now authorized to change its value each time the system enters into a new stratum. This framework is motivated by several applications arising in the context of aerospace engineering or in epidemiology (typically when a loss of control occurs). In this presentation, we give the necessary optimality conditions in this framework in the spirit of a hybrid maximum principle. The necessary optimality conditions involve a jump of the covector at the interface between two strata and also an averaged gradient condition related to the regionally switching parameter. We shall also give some insights how to obtain such a result using needle’s type variations.