Aggregative control of competitive agents with coupled quadratic costs and shared constraints

We consider the problem to control a large population of noncooperative heterogeneous agents, each with strongly convex quadratic cost function depending on the average population state, and all sharing a convex constraint, towards a competitive equilibrium. We assume a minimal information structure through which a central controller can broadcast incentive signals to control the decentralized optimal responses of the agents. We propose a model-free dynamic control law that, based on monotone operator theory arguments, ensures global convergence to an equilibrium independently on the parameters defining the quadratic cost functions, nor on the convex constraints.