Decentralized Convergence to Nash Equilibria in Constrained Deterministic Mean Field Control
It solves the problem of decentralized control under heterogeneous constraints for large populations, which is a novel extension of mean field game theory.
This paper extends deterministic mean field control to heterogeneous convex constraints, proposing decentralized model-free feedback iterations that provably converge to mean field Nash equilibria. The methods are validated on constrained linear quadratic and electric vehicle charging problems.
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.