Avis de Soutenance
Monsieur Laurent PFEIFFER
Soutiendra publiquement ses travaux d’habilitation à diriger les recherches
« Optimal control of PDEs: feedback laws and mean-field games »
Soutenance prévue le vendredi 24 janvier 2025 à 14h
Lieu : Théâtre Rousseau – Bâtiment Bouygues
CentraleSupélec 9 Rue Joliot-Curie 91190 Gif-sur-Yvette
Commission:
– Piermarco Cannarsa, professeur à l’Université de Rome « Tor Vergata » (examinateur)
– Pierre Cardaliaguet, professeur à l’Université Paris-Dauphine (examinateur)
– Diogo Gomes, professeur à la King Abdullah University of Sciences and Technology (rapporteur)
– Quentin Mérigot, professeur à l’Université Paris-Saclay (rapporteur)
– Emmanuel Trélat, professeur à Sorbonne Université (rapporteur)
– Hasnaa Zidani, professeure à l’INSA Rouen Normandie (examinatrice).
Abstract: I will present my main contributions around two independent topics, related to the optimal control of infinite-dimensional systems. The first part of the presentation will focus on the approximation of optimal feedback laws for stabilization problems. Optimal feedback laws can be characterized with the help of the Hamilton-Jacobi-Bellman (HJB) equation, but this characterization does not lead to a tractable numerical method, except in the linear-quadratic case, where it boils down to a Riccati equation. We will present our contributions the implementation and convergence analysis of Albrekht’s method, which bridges the HJB and the Riccati approaches.
The second part of the presentation will be devoted to mean-field game models: these are asymptotic Nash equilibrium models involving a very large number of agents, evolving according to deterministic or stochastic dynamics. We give existence and regularity results for a class of models in which agents interact via their control. We exploit the potential structure of these models, which can be reduced to optimal control problems of the Fokker-Planck equation. Finally, we demonstrate the effectiveness of an iterative numerical method based on the Frank-Wolfe algorithm.
