Feedback control via inertial manifolds for nonautonomous evolution equations
type: Item
instance of: scholarly article
title: Feedback control via inertial manifolds for nonautonomous evolution equations
zbMATH Open document ID: 1238.34093
author: Norbert Koksch
author: S. Siegmund
published in: Communications on Pure and Applied Analysis
publication date: 2011-12-19T00:00:00Z
review text: In [Lect. Notes Control Inf. Sci. 154, 22--27 (1991; Zbl 0742.93030)], \textit{P. Brunovský} suggested a method to control the dynamics of evolution equations using finite-dimenstional controllers. The authors of the present paper extend these results to nonautonomous evolution equations. This is based on their earlier results on constructing corresponding inertial manifolds (i.e., finite-dimensional attractive invariant manifolds) using the graph transform rather than the Lyapunov-Perron method. In particular, they obtain inertial manifolds of lower dimension, as illustrated using two examples.
Mathematics Subject Classification ID: 34C45
Mathematics Subject Classification ID: 34D45
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 35B42
Mathematics Subject Classification ID: 37C60
Mathematics Subject Classification ID: 34H05
zbMATH DE Number: 5989641
zbMATH Keywords: inertial manifold
zbMATH Keywords: nonautonomous dynamical system
zbMATH Keywords: feedback control
reviewed by: Christian Pötzsche
MaRDI profile type: Publication
full work available at URL: cpaa.2011.10.917
OpenAlex ID: W2324567675
DOI: 10.3934/CPAA.2011.10.917
description: scientific article; zbMATH DE number 5989641