  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.
