Hybrid maximum principle with regionally switching parameter - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

Hybrid maximum principle with regionally switching parameter

(1) , (1) , (2)
1
2
Anas Bouali
  • Function : Author
  • PersonId : 1132322
Loïc Bourdin

Abstract

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.
Fichier principal
Vignette du fichier
HMP with with regionally switching parameter.pdf (739.52 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03638701 , version 1 (12-04-2022)

Identifiers

  • HAL Id : hal-03638701 , version 1

Cite

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

Share

Gmail Facebook Twitter LinkedIn More