Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Carlo Orrieri, Dipartimento di Matematica, Sapienza Università di Roma
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. Savarè