A Pontryagin Maximum Principle in Wasserstein spaces for constrained optimal control problems
By Benoît Bonnet. E S A I M: Control, Optimisation and Calculus of Variations, 2018
51 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/833b3d1a8a6f0f48f8ec3a212a41801ea09484dd
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Citations in the corpus
- Differential inclusions in Wasserstein spaces: The Cauchy-Lipschitz framework (2020, background): “While a few results have been dealing with controllability properties of continuity equations [36, 37], the major part of the literature has been devoted to the study of optimal control problems, with contributions ranging from existence results [23, 38, 39, 40] and necessary optimality conditions [”
- Necessary Optimality Conditions for Optimal Control Problems in Wasserstein Spaces (2021, methodology): “[9,11,15,42] and [17,37] in connection with the theory ofmean-field games.”