Accepted Paper

Inserted: 1 apr 2025
Last Updated: 22 feb 2026

Journal: Siam Journal on Control and Optimization
Year: 2026

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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