A Pontryagin Maximum Principle in Wasserstein Spaces for Constrained Optimal Control Problems
Optimization and Control
2019-10-22 v9
Abstract
In this paper, we prove a Pontryagin Maximum Principle for constrained optimal control problems in the Wasserstein space of probability measures. The dynamics, is described by a transport equation with non-local velocities and is subject to end-point and running state constraints. Building on our previous work, we combine the classical method of needle-variations from geometric control theory and the metric differential structure of the Wasserstein spaces to obtain a maximum principle stated in the so-called Gamkrelidze form.
Cite
@article{arxiv.1810.13117,
title = {A Pontryagin Maximum Principle in Wasserstein Spaces for Constrained Optimal Control Problems},
author = {Benoît Bonnet},
journal= {arXiv preprint arXiv:1810.13117},
year = {2019}
}
Comments
35 pages