Volume 25, 2019
|Number of page(s)||38|
|Published online||18 October 2019|
A Pontryagin Maximum Principle in Wasserstein spaces for constrained optimal control problems*
Aix Marseille Université, CNRS, ENSAM, Université de Toulon, LIS,
** Corresponding author: firstname.lastname@example.org
Accepted: 13 July 2019
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 which are affine in the control, 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 formulated in the so-called Gamkrelidze form.
Mathematics Subject Classification: 49K20 / 49K27 / 58E25
Key words: Pontryagin Maximum Principle / Wasserstein spaces / metric differential calculus / needle-like variations / state constraints
This research is partially supported by the Padua University grant SID 2018 “Controllability, stabilizability and infimun gaps for control systems”, prot. BIRD 187147. The author was supported by the Archimède Labex (ANR-11-LABX-0033), by the A*MIDEX project (ANR- 11-IDEX-0001-02), funded by the “Investissements d'Avenir” French Government program managed by the French National Research Agency (ANR), and by the SRGI ANR Grant ANR-15-CE40-0018.
The author is indebted to the anonymous reviewers for their careful reading and the many comments they provided that greatly improved the manuscript.
© The authors. Published by EDP Sciences, SMAI 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://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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