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Balanced truncation of linear second-order systems: a Hamiltonian approach

Journal Article


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Abstract


  • We present a formal procedure for structure-preserving model reduction of linear

    second-order and Hamiltonian control problems that appear in a variety of physical contexts, e.g.,

    vibromechanical systems or electrical circuit design. Typical balanced truncation methods that

    project onto the subspace of the largest Hankel singular values fail to preserve the problem’s physical

    structure and may suffer from lack of stability. In this paper, we adopt the framework of generalized

    Hamiltonian systems that covers the class of relevant problems and that allows for a generalization of

    balanced truncation to second-order problems. It turns out that the Hamiltonian structure, stability,

    and passivity are preserved if the truncation is done by imposing a holonomic constraint on the system

    rather than standard Galerkin projection.

Authors


  •   Hartmann, Carsten (external author)
  •   Wheeler, V.-M
  •   Schutte, Christof (external author)

Publication Date


  • 2010

Geographic Focus


Citation


  • Hartmann, C., Vulcanov, V. & Schutte, C. (2010). Balanced truncation of linear second-order systems: a Hamiltonian approach. SIAM: Multiscale Modeling and Simulation, 8 (4), 1348-1367.

Scopus Eid


  • 2-s2.0-77956763488

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1553&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/547

Has Global Citation Frequency


Number Of Pages


  • 19

Start Page


  • 1348

End Page


  • 1367

Volume


  • 8

Issue


  • 4

Place Of Publication


  • United States

Abstract


  • We present a formal procedure for structure-preserving model reduction of linear

    second-order and Hamiltonian control problems that appear in a variety of physical contexts, e.g.,

    vibromechanical systems or electrical circuit design. Typical balanced truncation methods that

    project onto the subspace of the largest Hankel singular values fail to preserve the problem’s physical

    structure and may suffer from lack of stability. In this paper, we adopt the framework of generalized

    Hamiltonian systems that covers the class of relevant problems and that allows for a generalization of

    balanced truncation to second-order problems. It turns out that the Hamiltonian structure, stability,

    and passivity are preserved if the truncation is done by imposing a holonomic constraint on the system

    rather than standard Galerkin projection.

Authors


  •   Hartmann, Carsten (external author)
  •   Wheeler, V.-M
  •   Schutte, Christof (external author)

Publication Date


  • 2010

Geographic Focus


Citation


  • Hartmann, C., Vulcanov, V. & Schutte, C. (2010). Balanced truncation of linear second-order systems: a Hamiltonian approach. SIAM: Multiscale Modeling and Simulation, 8 (4), 1348-1367.

Scopus Eid


  • 2-s2.0-77956763488

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1553&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/547

Has Global Citation Frequency


Number Of Pages


  • 19

Start Page


  • 1348

End Page


  • 1367

Volume


  • 8

Issue


  • 4

Place Of Publication


  • United States