A Pontryagin Maximum Principle in Wasserstein Spaces for Constrained Optimal Control Problems

Benoît Bonnet

doi:10.1051/cocv/2019044

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arXiv · 1810.13117

A Pontryagin Maximum Principle in Wasserstein Spaces for Constrained Optimal Control Problems

Benoît Bonnet

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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.

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BibTeX RIS

Benoît Bonnet. 2019-10-19. A Pontryagin Maximum Principle in Wasserstein Spaces for Constrained Optimal Control Problems. https://doi.org/10.1051/cocv%2F2019044

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