Mean-Field First Order Optimality Condition under Low Regularity of Controls
Abstract
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.
Fields of Study & Subjects
Distributed Control Multi-Agent Systems
Markov Chains and Monte Carlo Methods
Mathematical Biology Tumor Growth
Publication details
- Journal / source
- SIAM Journal on Control and Optimization
- Volume
- 64
- Issue
- 4
- Pages
- 2973–2999
- Publication date
- 29 July 2026
- Language
- EN