Structure-preserving approximation of distributed-parameter second-order systems using Krylov subspaces

In this article, the approximation of linear second-order distributed-parameter systems (DPS) is considered using a Galerkin approach. The resulting finite-dimensional approximation model also has a second-order structure and preserves the stability as well as the passivity. Furthermore, by extendin...

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Published inMathematical and computer modelling of dynamical systems Vol. 20; no. 4; pp. 395 - 413
Main Authors Deutscher, J., Harkort, Ch
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 04.07.2014
Taylor & Francis Ltd
Subjects
Approximation
Dynamical systems
Dynamics
Euler-Bernoulli beams
Galerkin approach
Galerkin methods
Krylov subspace methods
linear distributed-parameter systems
Mathematical analysis
Mathematical models
moment matching
Preserves
second-order systems
structure preservation
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Abstract In this article, the approximation of linear second-order distributed-parameter systems (DPS) is considered using a Galerkin approach. The resulting finite-dimensional approximation model also has a second-order structure and preserves the stability as well as the passivity. Furthermore, by extending the Krylov subspace methods for finite-dimensional systems of second order to DPS, the basis vectors of the Galerkin projection are determined such that the transfer behaviour of the DPS can be approximated by using moment matching. The structure-preserving approximation of an Euler-Bernoulli beam with Kelvin-Voigt damping demonstrates the results of the article.
AbstractList In this article, the approximation of linear second-order distributed-parameter systems (DPS) is considered using a Galerkin approach. The resulting finite-dimensional approximation model also has a second-order structure and preserves the stability as well as the passivity. Furthermore, by extending the Krylov subspace methods for finite-dimensional systems of second order to DPS, the basis vectors of the Galerkin projection are determined such that the transfer behaviour of the DPS can be approximated by using moment matching. The structure-preserving approximation of an Euler-Bernoulli beam with Kelvin-Voigt damping demonstrates the results of the article.
In this article, the approximation of linear second-order distributed-parameter systems (DPS) is considered using a Galerkin approach. The resulting finite-dimensional approximation model also has a second-order structure and preserves the stability as well as the passivity. Furthermore, by extending the Krylov subspace methods for finite-dimensional systems of second order to DPS, the basis vectors of the Galerkin projection are determined such that the transfer behaviour of the DPS can be approximated by using moment matching. The structure-preserving approximation of an Euler-Bernoulli beam with Kelvin-Voigt damping demonstrates the results of the article. [PUBLICATION ABSTRACT]
Author Harkort, Ch
Deutscher, J.
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Cites_doi 10.1137/0326041
10.1080/13873950701844170
10.1023/A:1024052419431
10.1109/CDC.2005.1582501
10.1109/TAC.2010.2090063
10.1007/978-1-4612-4224-6
10.1016/j.laa.2004.12.013
10.1007/978-1-4471-0419-3
10.1007/978-3-642-85949-6
10.1007/978-3-642-66282-9
10.1016/j.sysconle.2008.10.016
10.1137/040605552
10.1137/1.9780898718713
10.1109/9.544000
10.1017/S0962492902000120
10.2514/3.55187
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References CIT0010
CIT0021
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CIT0011
Grimme E.J. (CIT0007) 1997
Chahlaoui Y. (CIT0002) 2002
Kato T. (CIT0022) 1995
Benner P. (CIT0004) 2012
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Reis T. (CIT0013)
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CIT0019
References_xml – volume-title: Structure-preserving order reduction of large scale second-order models
  year: 2005
  ident: CIT0015
  contributor:
    fullname: Salimbahrami B.
– ident: CIT0019
  doi: 10.1137/0326041
– volume-title: Proc. Int. Symp. on Mathematical Theory of Networks and Systems
  year: 2002
  ident: CIT0002
  contributor:
    fullname: Chahlaoui Y.
– ident: CIT0003
  doi: 10.1080/13873950701844170
– volume-title: Finite-rank ADI iteration for operator Lyapunov equations
  ident: CIT0013
  contributor:
    fullname: Reis T.
– ident: CIT0020
  doi: 10.1023/A:1024052419431
– ident: CIT0011
  doi: 10.1109/CDC.2005.1582501
– ident: CIT0014
  doi: 10.1109/TAC.2010.2090063
– ident: CIT0017
  doi: 10.1007/978-1-4612-4224-6
– ident: CIT0008
  doi: 10.1016/j.laa.2004.12.013
– ident: CIT0018
  doi: 10.1007/978-1-4471-0419-3
– volume-title: An Improved Numerical Method for Balanced Truncation for Symmetric Second-Order Systems
  year: 2012
  ident: CIT0004
  contributor:
    fullname: Benner P.
– ident: CIT0016
  doi: 10.1007/978-3-642-85949-6
– volume-title: Perturbation Theory for Linear Operators
  year: 1995
  ident: CIT0022
  doi: 10.1007/978-3-642-66282-9
  contributor:
    fullname: Kato T.
– ident: CIT0012
  doi: 10.1016/j.sysconle.2008.10.016
– volume-title: Krylov projection methods for model reduction
  year: 1997
  ident: CIT0007
  contributor:
    fullname: Grimme E.J.
– ident: CIT0010
  doi: 10.1137/040605552
– ident: CIT0005
  doi: 10.1137/1.9780898718713
– ident: CIT0001
  doi: 10.1109/9.544000
– ident: CIT0006
  doi: 10.1017/S0962492902000120
– ident: CIT0021
  doi: 10.2514/3.55187
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Snippet In this article, the approximation of linear second-order distributed-parameter systems (DPS) is considered using a Galerkin approach. The resulting...
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SubjectTerms Approximation
Dynamical systems
Dynamics
Euler-Bernoulli beams
Galerkin approach
Galerkin methods
Krylov subspace methods
linear distributed-parameter systems
Mathematical analysis
Mathematical models
moment matching
Preserves
second-order systems
structure preservation
Title Structure-preserving approximation of distributed-parameter second-order systems using Krylov subspaces
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