Adrien Séguret (EDF R&D /  CEREMADE, Université Paris Dauphine - PSL) 

Title : A Mean Field Control problem of Piecewise Deterministic Markov Processes and its application to smart charging

Abstract : In this talk, I will present a mean field control problem of Piecewiece Deterministic Markov Processes (PDMP). While this kind of process is largely used in molecular biology and in system reliability and maintenance, this work is motivated by its potential application in the optimal charge of a large fleet of electrical vehicles (EVs). A Lagrangian approach is proposed to decompose the problem. Although the mean field control problem is not convex, it is proved to achieve zero duality gap. A stochastic version of the Uzawa algorithm is shown to converge to the primal solution.This algorithm is used in a numerical simulation to coordinate the charging of a large fleet of EVs in order to track a target consumption profile. 

Then, a PDE formulation of the mean field control problem is introduced, with additional congestion constraints.  The characterization of the minizers is given and a numerical approximation of the problem is presented in a smart charging context.