{"ID":2894053,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.12411","arxiv_id":"2507.12411","title":"Linearization-Based Feedback Stabilization of McKean-Vlasov PDEs","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 Schrodinger-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.","short_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 t...","url_abs":"https://arxiv.org/abs/2507.12411","url_pdf":"https://arxiv.org/pdf/2507.12411v3","authors":"[\"Dante Kalise\",\"Lucas M. Moschen\",\"Grigorios A. Pavliotis\"]","published":"2025-07-16T16:59:49Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math-ph\",\"math.NA\"]","methods":"[]","has_code":false}