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arXiv · 1803.04689

Mean-field optimal control as Gamma-limit of finite agent controls

Massimo Fornasier·Stefano Lisini·Carlo Orrieri·Giuseppe Savaré
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Abstract

This paper focuses on the role of a government of a large population of interacting agents as a mean field optimal control problem derived from deterministic finite agent dynamics. The control problems are constrained by a PDE of continuity-type without diffusion, governing the dynamics of the probability distribution of the agent population. We derive existence of optimal controls in a measure-theoretical setting as natural limits of finite agent optimal controls without any assumption on the regularity of control competitors. In particular, we prove the consistency of mean-field optimal controls with corresponding underlying finite agent ones. The results follow from a $\Gamma$-convergence argument constructed over the mean-field limit, which stems from leveraging the superposition principle.

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Massimo Fornasier, Stefano Lisini, Carlo Orrieri, Giuseppe Savaré. 2018-03-13. Mean-field optimal control as Gamma-limit of finite agent controls. https://arxiv.org/abs/1803.04689

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