| Issue |
ESAIM: ProcS
Volume 71, 2021
FGS’2019 - 19th French-German-Swiss conference on Optimization
|
|
|---|---|---|
| Page(s) | 21 - 32 | |
| DOI | https://doi.org/10.1051/proc/202171103 | |
| Published online | 01 September 2021 | |
Penalty function method for the minimal time crisis problem
1 MISTEA, Univ. Montpellier, INRAE, Institut Agro (UMR 729), 34060 Montpellier, France .
kenza.boumaza@inrae.fr
2 Avignon Université, Laboratoire de Mathématiques d’Avignon (EA 2151), 84018 Avignon, France .
terence.bayen@univ-avignon.fr
3 MISTEA, Univ. Montpellier, INRAE, Institut Agro (UMR 729), 34060 Montpellier, France .
alain.rapaport@inrae.fr
In this note, we propose a new method to approximate the minimal time crisis problem using an auxiliary control and a penalty function, and show its convergence to a solution to the original problem. The interest of this approach is illustrated on numerical examples for which optimal trajectories can leave and enter the crisis set tangentially.
Résumé
Dans cette note, nous proposons une nouvelle méthode pour approcher le problème du temps de crise en introduisant un contrôle additionnel et une fonction de pénalisation. Nous montrons la convergence des solutions approchées vers une solution du problème original. L’intérêt de cette approche est illustrée sur un exemple numérique pour lequel les trajectoires optimales peuvent entrer ou sortir tangentiellement de l’ensemble de crise.
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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