Time: March 28, 2025, 11:00
Room: RICAM, SP2 416-1

Titel: Optimal Control of Densities: Deflation and Stabilization for Large-Scale Interacting Particle Systems

Abstract: 

This talk explores novel approaches to optimization and control of large-scale agent-based models. We first examine McKean-Vlasov PDEs that govern the mean-field evolution of interacting particle systems, demonstrating how nonlinear transport and Hamilton-Jacobi-Bellman equations serve as fundamental building blocks across various applications.

In the first part, we present a numerical framework combining spectral methods and deflation operators to compute multiple steady states of McKean-Vlasov equations. This approach enables us to identify both stable and unstable equilibria, particularly in systems exhibiting phase transitions. We then develop optimal control strategies to stabilize the system toward these equilibria, including unstable ones, implementing the control through a receding horizon approach.

The second part explores connections between this framework and related problems in mean-field games, optimal transport, Schrödinger bridges, and Wasserstein gradient flows. We highlight a unified variational perspective that encompasses these seemingly disparate fields, with applications ranging from pedestrian dynamics to collective animal behavior.