Decentralized Convergence to Nash Equilibria in Constrained Deterministic Mean Field Control

TL;DR

This paper develops decentralized methods for large populations of agents with constraints to find Nash equilibria in mean field control problems, extending existing theories to constrained scenarios.

Contribution

It introduces novel decentralized feedback algorithms for constrained mean field control, addressing heterogeneity and convex constraints in large agent populations.

Findings

Successfully computed mean field Nash equilibria in constrained settings

Applied methods to electric vehicle charging control

Demonstrated convergence in large-scale simulations

Abstract

This paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and affected by the aggregate behavior of the overall population. For such large-scale systems, the theory of aggregative and mean field games has been established and successfully applied in various scientific disciplines. While the existing literature addresses the case of unconstrained agents, we formulate deterministic mean field control problems in the presence of heterogeneous convex constraints for the individual agents, for instance arising from agents with linear dynamics subject to convex state and control constraints. We propose several model-free feedback iterations to compute in a decentralized fashion a mean field Nash equilibrium in the limit of infinite population size. We apply our methods to the constrained linear quadratic deterministic mean field control problem and to the constrained mean field charging control problem for large populations of plug-in electric vehicles.