Bi-objective finite horizon optimal control problems with Bolza and maximum running cost

Abstract : In this paper, we investigate optimal control problems with two objective functions of different nature that need to be minimized simultaneously. One objective is in the classical Bolza form and the other one is defined as a maximum running cost. Our approach is based on the Hamilton-Jacobi-Bellman framework. In the problem considered here the existence of Pareto solutions is not guaranteed. So first, we consider the bi-objective problem to be minimized over the convexified dynamical system. We show that if a vector is (weak) Pareto optimal solution for the convexified problem, then there exists an (weak) ε-Pareto optimal solution of the original problem that is in the neighborhood of this vector. After we define an auxiliary optimal control problem and show that the weak Pareto front of the convexified problem is a subset of the zero level set of the corresponding value function. Moreover, with a geometrical approach we establish a characterization of the Pareto front. It is also proved that the (weak) ε-Pareto front is contained in the negative level set of the auxiliary optimal control problem that is less or equal ε. Some numerical examples are considered to show the relevance of our approach.
Type de document :
Pré-publication, Document de travail
2018
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01929094
Contributeur : Ana Paula Chorobura <>
Soumis le : mardi 20 novembre 2018 - 23:46:00
Dernière modification le : vendredi 30 novembre 2018 - 09:13:21

Fichier

Chorobura_and_Zidani.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01929094, version 1

Citation

Ana Chorobura, Hasnaa Zidani. Bi-objective finite horizon optimal control problems with Bolza and maximum running cost. 2018. 〈hal-01929094〉

Partager

Métriques

Consultations de la notice

16

Téléchargements de fichiers

27