Mean field limits for controlled system
Résumé
In this talk, I will explain how to extend classical mean field methods to study the control and the optimal control of large stochastic systems. I will first show that as the number of objects of the system grows, solving an optimal control problem for a stochastic system can be reduced to the solving of a deterministic optimization problem. Then, I will present how to study the limiting behavior of the controlled system using di fferential inclusions. In practice, this allows one to easily evaluate the performance of a policy and provide a way to asymptotically solve problems that used to be intractable. Some examples will be provided, illustrating these facts.