Boundary Control for a Kind of Coupled PDE-ODE System

Boundary Control for a Kind of Coupled PDE-ODE System

A coupled system of an ordinary differential equation (ODE) and a heat partial differential equation (PDE) with spatially varying coefficients is discussed. By using the PDE backstepping method, the state-feedback stabilizing controller is explicitly constructed with the assumptions λ(x)∈P[x]n and λ...

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Main Authors: Yuanting Wang, Fucheng Liao, Yonglong Liao, Zhengwei Shen
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Control Science and Engineering
Online Access:http://dx.doi.org/10.1155/2014/946736
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spelling doaj-205e9b6f783249e494ba3cda511b67cd2020-11-25T00:50:44ZengHindawi LimitedJournal of Control Science and Engineering1687-52491687-52572014-01-01201410.1155/2014/946736946736Boundary Control for a Kind of Coupled PDE-ODE SystemYuanting Wang0Fucheng Liao1Yonglong Liao2Zhengwei Shen3School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaSchool of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaSchool of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaSchool of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaA coupled system of an ordinary differential equation (ODE) and a heat partial differential equation (PDE) with spatially varying coefficients is discussed. By using the PDE backstepping method, the state-feedback stabilizing controller is explicitly constructed with the assumptions λ(x)∈P[x]n and λ(x)∈C[0, l]∞, respectively. The closed-loop system is proved to be exponentially stable by this controller. A simulation example is presented to illustrate the effectiveness of the proposed method.http://dx.doi.org/10.1155/2014/946736
collection DOAJ
language English
format Article
sources DOAJ
author Yuanting Wang
Fucheng Liao
Yonglong Liao
Zhengwei Shen
spellingShingle Yuanting Wang
Fucheng Liao
Yonglong Liao
Zhengwei Shen
Boundary Control for a Kind of Coupled PDE-ODE System
Journal of Control Science and Engineering
author_facet Yuanting Wang
Fucheng Liao
Yonglong Liao
Zhengwei Shen
author_sort Yuanting Wang
title Boundary Control for a Kind of Coupled PDE-ODE System
title_short Boundary Control for a Kind of Coupled PDE-ODE System
title_full Boundary Control for a Kind of Coupled PDE-ODE System
title_fullStr Boundary Control for a Kind of Coupled PDE-ODE System
title_full_unstemmed Boundary Control for a Kind of Coupled PDE-ODE System
title_sort boundary control for a kind of coupled pde-ode system
publisher Hindawi Limited
series Journal of Control Science and Engineering
issn 1687-5249
1687-5257
publishDate 2014-01-01
description A coupled system of an ordinary differential equation (ODE) and a heat partial differential equation (PDE) with spatially varying coefficients is discussed. By using the PDE backstepping method, the state-feedback stabilizing controller is explicitly constructed with the assumptions λ(x)∈P[x]n and λ(x)∈C[0, l]∞, respectively. The closed-loop system is proved to be exponentially stable by this controller. A simulation example is presented to illustrate the effectiveness of the proposed method.
url http://dx.doi.org/10.1155/2014/946736
work_keys_str_mv AT yuantingwang boundarycontrolforakindofcoupledpdeodesystem
AT fuchengliao boundarycontrolforakindofcoupledpdeodesystem
AT yonglongliao boundarycontrolforakindofcoupledpdeodesystem
AT zhengweishen boundarycontrolforakindofcoupledpdeodesystem
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