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.

arXiv comment35 pages

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Cited by in corpus (6)

• Minimal time for the continuity equation controlled by a localized perturbation of the velocity vector field
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• Dynamic Programming in Probability Spaces via Optimal Transport
• Vanishing viscosity in mean-field optimal control
• A Pontryagin Maximum Principle for agent-based models with convex state space
• First-order Conditions for Optimization in the Wasserstein Space