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Seminario di Equazioni Differenziali e Applicazioni: “Mean field type control with congestion”

Martedì 20 Giugno 2017, ore 12:00 - Aula 2BC60 - Mathieu Lauriere

ARGOMENTI: Seminars

Martedì 20 Giugno 2017 alle ore 12:00 in Aula 2BC60, Mathieu Lauriere (NYU Shangai) terrà un seminario dal titolo “Mean field type control with congestion”.

Abstract
The theory of mean field type control aims at describing the behaviour of a large number of interacting agents using a common feedback. A phenomenon that have raised a lot of interest recently concerns congestion effects, where the agents try to avoid crowded regions. One way to take into account such effects is to let the cost of displacement increase in the regions where the density is large. We will present a system of partial differential equations (PDE) arising in this setting: a forward Fokker-Planck equation and a backward Hamilton-Jacobi-Bellman equation describe respectively the evolution of the density of agents and of the value function. We are able to prove the existence and uniqueness of suitably defined weak solutions, which are characterized as the optima of two optimal control problems in duality. This optimal control point of view also leads to a numerical method to solve the PDE system. We will present an algorithm based on an augmented Lagrangian method. Numerical results will be presented. This is joint work with Yves Achdou.

Rif. Int. M. Bardi, P. Mannucci, C. Marchi

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