| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 9 | |
| Number of page(s) | 38 | |
| DOI | https://doi.org/10.1051/cocv/2022089 | |
| Published online | 19 January 2023 | |
A general comparison principle for Hamilton Jacobi Bellman equations on stratified domains
1
UMA, ENSTA Paris, Institut Polytechnique de Paris,
91120
Palaiseau,
France
2
Normandie Univ, INSA Rouen Normandie, Laboratoire LMI,
76000
Rouen,
France
* Corresponding author: hasnaa.zidani@insa-rouen.fr
Received:
29
October
2021
Accepted:
20
December
2022
This manuscript aims to study finite horizon, first order Hamilton Jacobi Bellman equations on stratified domains. This problem is related to optimal control problems with discontinuous dynamics. We use nonsmooth analysis techniques to derive a strong comparison principle as in the classical theory and deduce that the value function is the unique viscosity solution. Furthermore, we prove some stability results of the Hamilton Jacobi Bellman equation. Finally, we establish a general convergence result for monotone numerical schemes in the stratified case.
Mathematics Subject Classification: 49J53 / 35F21 / 49L25
Key words: Nonsmooth analysis / invariance principles / viscosity theory / Hamilton Jacobi equations
© The authors. Published by EDP Sciences, SMAI 2023
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.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.