Linearization-based feedback stabilization of McKean-Vlasov PDEs
File(s)
Accepted version
Author(s)
Kalise, Dante
Moschen, Lucas
Pavliotis, Greg
Type
Journal Article
Abstract
We develop a feedback control framework for stabilizing the McKean-Vlasov PDE on the torus. Our goal is to steer the dynamics toward a prescribed stationary distribution or accelerate convergence to it using a time-dependent control potential. We reformulate the controlled PDE in
a weighted, zero-mean space and apply the ground-state transform to obtain a Schr¨odinger-type operator. The resulting operator framework enables spectral analysis, verification of the infinite dimensional Hautus test, and construction of a Riccati-based feedback law derived from the linearized dynamics, yielding local exponential stabilization with a chosen convergence rate. We rigorously prove local exponential stabilization via maximal regularity arguments and nonlinear estimates.
Numerical experiments on well-studied models in one and two dimensions (the noisy Kuramoto model for synchronization, the O(2) spin model in a magnetic field, and the von Mises attractive interaction potential) showcase the effectiveness of our control strategy, demonstrating convergence acceleration and stabilization of unstable equilibria.
a weighted, zero-mean space and apply the ground-state transform to obtain a Schr¨odinger-type operator. The resulting operator framework enables spectral analysis, verification of the infinite dimensional Hautus test, and construction of a Riccati-based feedback law derived from the linearized dynamics, yielding local exponential stabilization with a chosen convergence rate. We rigorously prove local exponential stabilization via maximal regularity arguments and nonlinear estimates.
Numerical experiments on well-studied models in one and two dimensions (the noisy Kuramoto model for synchronization, the O(2) spin model in a magnetic field, and the von Mises attractive interaction potential) showcase the effectiveness of our control strategy, demonstrating convergence acceleration and stabilization of unstable equilibria.
Date Acceptance
2026-07-10
Citation
SIAM Journal of Control and Optimization
ISSN
0363-0129
Publisher
Society for Industrial and Applied Mathematics
Journal / Book Title
SIAM Journal of Control and Optimization
Copyright Statement
Copyright This paper is embargoed until publication. Once published the author’s accepted manuscript will be made available under a CC-BY License in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy).
License URL
Publication Status
Accepted