Speaker:

Mathieu Laurière (Université Paris Diderot)

Title:

Mean field type control with congestion

Abstract: The theory of mean field type control, developed mainly by Bensoussan, Frehse and Yam, aims at describing the behaviour of a large number of interacting agents using a common feedback. A type of problems that have raised a lot of interest recently concerns congestion effects. These problems model situations in which the cost of displacement of the agents increases in the regions where the density is large (as, for instance, in crowd motion). I will explain how we obtain existence and uniqueness of suitably defined weak solutions for a system of partial differential equations arising in this setting. The solutions are characterized as the optima of two optimal control problems in duality. Moreover, to solve this problem numerically, a method based on an augmented Lagrangian approach will be presented, and numerical results will be provided.