- Series
- PDE Seminar
- Time
- Tuesday, February 25, 2025 - 3:30pm for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Samuel Daudin – Université Paris Cité – samuel.daudin@u-paris.fr – https://scholar.google.com/citations?user=st-P3d0AAAAJ&hl=fr
- Organizer
- Lukas Wessels
The aim of this talk is to discuss recent advances around the convergence problem in mean field control theory and the study of associated nonlinear PDEs.
We are interested in optimal control problems involving a large number of interacting particles and subject to independent Brownian noises. As the number of particles tends to infinity, the problem simplifies into a McKean-Vlasov type optimal control problem for a typical particle. I will present recent results concerning the quantitative analysis of this convergence. More precisely, I will discuss an approach based on the analysis of associated value functions. These functions are solutions of Hamilton-Jacobi equations in high dimension and the convergence problem translates into a stability problem for the limit equation which is posed on a space of probability measures.
I will also discuss the well-posedness of this limiting equation, the study of which seems to escape the usual techniques for Hamilton-Jacobi equations in infinite dimension.