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Rapid Fredholm stabilization of the Kuramoto--Sivashinsky equation with unrestricted, spatially-varying anti-diffusion

L5 · ResearcherResearcharXiv· 10/6/2026

Advances mathematical control theory using machine learning techniques for PDE stabilization

AI Summary

Researchers develop a novel feedback control method using neural operators to stabilize the Kuramoto-Sivashinsky equation with spatially-varying anti-diffusion coefficients.

Excerpt

We develop the first feedback design for rapid stabilization of the Kuramoto--Sivashinsky equation with a spatially varying anti-diffusion coefficient. For constant coefficients, the single-input Fredholm design of Coron and Lü (2015) excludes a discrete set of values at which repeated unstable eigenvalues cause a loss of controllability. We overcome this obstruction by introducing a second boundary input and assigning the two inputs distinct roles. The key idea, inspired by Heymann's Lemma, is

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