English

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.

Keywords

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

R2 v1 2026-06-23T04:58:40.345Z