Distributed control of the generalized Korteweg-de Vries-Burgers equation
type: Item
instance of: scholarly article
title: Distributed control of the generalized Korteweg-de Vries-Burgers equation
zbMATH Open document ID: 1151.76410
DOI: 10.1155/2008/621672
author: Nejib Smaoui
author: Rasha H. Al-Jamal
published in: Mathematical Problems in Engineering
publication date: 2008-11-24T00:00:00Z
full work available at URL: https://eudml.org/doc/54831
review text: Summary: The paper deals with the distributed control of the generalized Kortweg-de Vries-Burgers equation (GKdVB) subject to periodic boundary conditions via Karhunen-Loève (K-L) Galerkin method. The decomposition procedure of the K-L method is presented to illustrate the use of this method in analyzing numerical simulations data which represent the solutions to GKdVB equation. The K-L Galerkin projection is used as a model reduction technique for nonlinear systems to derive a system of ordinary differential equations (ODEs) that mimics the dynamics of the GKdVB equation. The data coefficients derived from the ODE system are then used to approximate the solutions of the GKdVB equation. Finally, three state feedback linearization control schemes with the objective of enhancing the stability of the GKdVB equation are proposed. Simulations of the controlled system are given to illustrate the developed theory.
Mathematics Subject Classification ID: 76B75
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 93C20
zbMATH DE Number: 5372481
zbMATH Keywords: Karhunen-Loève Galerkin method
zbMATH Keywords: ordinary differential equations
zbMATH Keywords: feedback linearization control
MaRDI profile type: Publication
OpenAlex ID: W1987359306
Wikidata QID: Q58646217
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description: scientific article; zbMATH DE number 5372481