Rapid Fredholm stabilization of the Kuramoto--Sivashinsky equation with unrestricted, spatially-varying anti-diffusion QVFHS1C9BW

URI	`m2://res/QVFHS1C9BW`
Kind	preprint
Creators	Luke Bhan, Miroslav Krstic, Yuanyuan Shi
Date	2026-10-06
Subjects	arxiv eess.SY, arxiv cs.LG, arxiv cs.SY, arxiv math.AP, arxiv math.OC
Scope	out

Expressions

e1: version, preprint

Date	2026-10-06
Ids	arXiv 2610.08764

Items in this resource

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

Item	Kind	Where	Source
Gain operator	definition	definition \thethrm	arxiv
Local existence and uniqueness for closed-loop plant	statement	proposition \thethrm	arxiv
Exponential stability of forced target system	statement	proposition \thethrm	arxiv
Gain-error bound	statement	lemma \thethrm	arxiv
Solutions of the closed loop	definition	definition \thethrm	arxiv
One input does not suffice	statement	proposition \thethrm	arxiv
The operator $\Gamma$	statement	lemma \thethrm	arxiv
Estimate of the nonlinear forcing term	statement	lemma \thethrm	arxiv
Admissible design	definition	definition \thethrm	arxiv
Spectral properties of original operator $\Aop$	statement	lemma \thethrm	arxiv
Kernel and gain exist, and the transformation is invertible	statement	theorem \thethrm	arxiv
High modes	statement	lemma \thethrm	arxiv
Neural-operator approximation	statement	theorem \thethrm	arxiv
Smoothing of $K$ and invertibility on modal spaces	statement	lemma \thethrm	arxiv
Design map is continuous, with uniformly bounded design constants	statement	theorem \thethrm	arxiv
Two inputs suffice for every $\lambda$	statement	theorem \thethrm	arxiv
Two boundary feedbacks stabilize the Kuramoto--Sivashinsky equation at any rate for every anti-diffusion coefficient	statement	theorem \thethrm	arxiv
Closed loop is locally exponentially stable under gain error	statement	theorem \thethrm	arxiv
Pre-feedback enables controllability for every $\lambda$	statement	theorem \thethrm	arxiv
Modal form of kernel equations	statement	proposition \thethrm	arxiv
Pre-feedback resolvent, spectrum, and input coefficients	statement	lemma \thethrm	arxiv
Closed loop is locally exponentially stable	statement	theorem \thethrm	arxiv
Kernel equations map plant to target	statement	proposition \thethrm	arxiv
A single neural operator stabilizes every plant in a compact class at a uniform rate	statement	theorem \thethrm	arxiv
ZR33M3Y70G	statement	lemma \thethrm	arxiv

Catalogue records

arxiv: 2610.08764 (work)