Dynamic Control of Agents Playing Aggregative Games With Coupling Constraints

We address the problem to control a population of noncooperative heterogeneous agents, each with convex cost function depending on the average population state, and all sharing a convex constraint, toward an aggregative equilibrium. We assume an information structure through which a central coordinator has access to the average population state and can broadcast control signals for steering the decentralized optimal responses of the agents. We design a dynamic control law that, based on operator theoretic arguments, ensures global convergence to an equilibrium independently on the problem data, that are the cost functions and the constraints, local and global, of the agents. We illustrate the proposed method in two application domains: Network congestion control and demand side management.