Mean Field Approximation of an Optimal Control Problem for the Continuity Equation Arising in Smart Charging

Abstract

We consider the optimal control of a finite population of hybrid processes (namely agents state is composed of a discrete and a continuous variable), modeling the optimal charging of a large population of identical plug-in electric vehicles (PEVs). We prove the convergence of the solution and that of the value of a sequence of finite population problems respectively to a solution and the value of a mean field optimal control problem.

Mean Field Game-Based Algorithms for Charging in Solar-Powered Parking Lots and Discharging into Homes a Large Population of Heterogeneous Electric Vehicles

“…In both [27,28], a rigorous justification was not given to guarantee that a solution will exist in the Nash equilibrium problem. More recently, the authors, in 2021 and 2023 [53,54], added constraints for battery charging and discharging in their mathematical formalism, and the authors in 2023 [55] they added behavioral considerations of the owners of electric vehicles (availability, planning, etc.) in their analysis.…”