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

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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Contributor : Benoît Bonnet <>
Submitted on : Monday, October 21, 2019 - 10:34:38 AM
Last modification on : Tuesday, October 22, 2019 - 1:45:35 AM

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Benoît Bonnet. A Pontryagin Maximum Principle in Wasserstein Spaces for Constrained Optimal Control Problems. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, In press, 25 (52), pp.38. ⟨10.1051/cocv/2019044 ⟩. ⟨hal-01937106v6⟩

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