Hybrid maximum principle with regionally switching parameter

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

In this paper we consider a Mayer optimal control problem governed by a hybrid control system defined over a partition of the state space. We assume that the control system depends on a regionally switching parameter that remains constant in each region but that can change its value when the state position crosses interfaces. This new framework allows to deal, as a particular case, with control systems including non-control regions. In this paper our objective is to provide the corresponding necessary optimality conditions in a Pontryagin form. Our approach is based on a thorough sensitivity analysis of the hybrid control system under needle-like perturbations of the control and under convex perturbations of the parameter. To this aim we invoke implicit function arguments to deal with the interface crossings that are assumed to be transverse. The paper is concluded with a simple academic example showing that our framework allows to fill a gap in the literature.

Mots clés: hybrid systems; optimal control; necessary optimality conditions; hybrid maximum principle; Pontryagin maximum principle; sensitivity analysis

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Térence Bayen, Anas Bouali, Loïc Bourdin. Hybrid maximum principle with regionally switching parameter. 2022. ⟨hal-03638701⟩