Preprint

Inserted: 1 apr 2025
Last Updated: 3 apr 2025

Year: 2025

Abstract:

We show that mean field optimal controls satisfy a first order optimality condition (at a.e. time) without any a priori requirement on their spatial regularity. This principle is obtained by a careful limit procedure of the Pontryagin maximum principle for finite particle systems. In particular, our result applies to the case of mean field selective optimal control problems for multipopulation and replicator dynamics.

Keywords: Pontryagin Maximum Principle, mean-field optimal control, agent-based systems, Low-regularity of controls

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