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arXiv · 2501.17674

Optimal Control of Nonlocal Balance Equations

Nikolay Pogodaev·Maxim Staritsyn
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Abstract

The paper presents an approach to studying optimal control problems in the space of nonnegative measures with dynamics given by a nonlocal balance law. This approach relies on transforming the balance law into a continuity equation in the space of probabilities, and subsequently into an ODE in a Hilbert space. The main result is a version of Pontryagin's maximum principle for the addressed problem, which encompasses all known formulations of this type in mean field control theory.

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Nikolay Pogodaev, Maxim Staritsyn. 2025-01-29. Optimal Control of Nonlocal Balance Equations. https://arxiv.org/abs/2501.17674

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