A Pontryagin Maximum Principle in Wasserstein spaces for constrained optimal control problems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 52.

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.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2019044
Classification : 49K20, 49K27, 58E25
Mots-clés : Pontryagin Maximum Principle, Wasserstein spaces, metric differential calculus, needle-like variations, state constraints
Bonnet, Benoît 1

1 
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Bonnet, Benoît. A Pontryagin Maximum Principle in Wasserstein spaces for constrained optimal control problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 52. doi : 10.1051/cocv/2019044. http://www.numdam.org/articles/10.1051/cocv/2019044/

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