Exponentially convergent decentralized charging control for large populations of plug-in electric vehicles

We address the problem to control the charging schedules in a large population of plug-in electric vehicles, considered as heterogeneous noncooperative agents, with different strongly convex quadratic cost functions weakly coupled by a common pricing signal, and convex charging constraints, e.g. plug-in times, deadlines and capacity limits. We assume a minimal information structure through which a central controller can broadcast incentive signals to coordinate the decentralized optimal responses of the agents. We propose a dynamic controller that, based on fixed point operator theory arguments, ensures global exponential convergence to an aggregative Nash equilibrium for large population size. We build upon the recent literature, further address general convex quadratic cost functions and convex constraints, and show exponential convergence without imposing technical assumptions. Finally, we illustrate the benefits of the proposed control law via numerical simulations, where the aggregate charging demand tends to fill the overnight demand valley.