A hybrid maximum principle including regional switching parameters.

par M. Anas BOUALI

vendredi 7 janv. 2022, 11:30 → 12:30 Europe/Paris

Visio (XLIM)

In this presentation, we consider a Bolza 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 regional 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). Our objective is to derive the necessary optimality conditions in this new framework in the spirit of a hybrid maximum principle. 

We shall see in this presentation how to obtain such conditions thanks to regional needle variations and to a careful sensitivity analysis in this hybrid setting.