Optimal Control of Nonlocal Balance Equations

2025/01/29 by Pogodaev, Nikolay, Staritsyn, Maxim
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2501.17674

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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