Dipartimento di Matematica, Sapienza Università di Roma         

Controlled Vlasov-type dynamics

Abstract: The aim of the talk is to connect the optimal control of Vlasov-type PDEs with large systems of controlled interacting particles/agents. The main difference towards the classical mean-field theory, where the particle are freely interacting with each other, is the presence of a central planner influencing the dynamics. In this situation it is not obvious that the mean field limit should commute with the optimization. In order to develop a rigorous  limit theory for this problem we employ the well-known concept of  Gamma convergence.

The talk is based on a work in project with M. Fornasier, S. Lisini and G. Savaré