A novel Krylov method for model order reduction of quadratic bilinear systems

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

Uittreksel

A novel Krylov subspace method is proposed to substantially reduce the computational complexity of the special class of quadratic bilinear dynamical systems. Based on the first two generalized transfer functions of the system, a Petrov-Galerkin projection scheme is applied. It is shown that such a projection amounts to interpolating the transfer functions at specific points which, in fact, is equivalent to constructing the corresponding Krylov subspace. For single-input single-output systems, the relevant Krylov subspace can be readily constructed for the interpolation points. For multi-input multi-output systems, also user-specified directional information is required so that a tangential interpolation can be determined. The method is demonstrated on a model of a nonlinear transmission line that is reduced from 100 to 10 states with a negligible relative error. In a second application the method is applied to the FitzHugh-Nagumo model.
TaalEngels
Titel2018 57th IEEE Conference on Decision and Control
UitgeverijInstitute of Electrical and Electronics Engineers (IEEE)
Pagina's3217-3222
Aantal pagina's6
DOI's
StatusGepubliceerd - dec 2018
Evenement57th IEEE Conference on Decision and Control, CDC 2018 - Miami, Verenigde Staten van Amerika
Duur: 17 dec 201819 dec 2018
Congresnummer: 57

Congres

Congres57th IEEE Conference on Decision and Control, CDC 2018
Verkorte titelCDC 2018
LandVerenigde Staten van Amerika
StadMiami
Periode17/12/1819/12/18

Vingerafdruk

transfer functions
interpolation
projection
SISO (control systems)
dynamical systems
transmission lines
output

Trefwoorden

    Citeer dit

    Cao, X., Maubach, J. M. L., Weiland, S., & Schilders, W. H. A. (2018). A novel Krylov method for model order reduction of quadratic bilinear systems. In 2018 57th IEEE Conference on Decision and Control (blz. 3217-3222). Institute of Electrical and Electronics Engineers (IEEE). DOI: 10.1109/CDC.2018.8619575
    Cao, X. ; Maubach, J.M.L. ; Weiland, S. ; Schilders, W.H.A./ A novel Krylov method for model order reduction of quadratic bilinear systems. 2018 57th IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers (IEEE), 2018. blz. 3217-3222
    @inproceedings{1b165844558745898302fdfe15acc78d,
    title = "A novel Krylov method for model order reduction of quadratic bilinear systems",
    abstract = "A novel Krylov subspace method is proposed to substantially reduce the computational complexity of the special class of quadratic bilinear dynamical systems. Based on the first two generalized transfer functions of the system, a Petrov-Galerkin projection scheme is applied. It is shown that such a projection amounts to interpolating the transfer functions at specific points which, in fact, is equivalent to constructing the corresponding Krylov subspace. For single-input single-output systems, the relevant Krylov subspace can be readily constructed for the interpolation points. For multi-input multi-output systems, also user-specified directional information is required so that a tangential interpolation can be determined. The method is demonstrated on a model of a nonlinear transmission line that is reduced from 100 to 10 states with a negligible relative error. In a second application the method is applied to the FitzHugh-Nagumo model.",
    keywords = "Model order reduction, Krylov methods, Quadratic-bilinear systems",
    author = "X. Cao and J.M.L. Maubach and S. Weiland and W.H.A. Schilders",
    year = "2018",
    month = "12",
    doi = "10.1109/CDC.2018.8619575",
    language = "English",
    pages = "3217--3222",
    booktitle = "2018 57th IEEE Conference on Decision and Control",
    publisher = "Institute of Electrical and Electronics Engineers (IEEE)",
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    }

    Cao, X, Maubach, JML, Weiland, S & Schilders, WHA 2018, A novel Krylov method for model order reduction of quadratic bilinear systems. in 2018 57th IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers (IEEE), blz. 3217-3222, Miami, Verenigde Staten van Amerika, 17/12/18. DOI: 10.1109/CDC.2018.8619575

    A novel Krylov method for model order reduction of quadratic bilinear systems. / Cao, X.; Maubach, J.M.L.; Weiland, S.; Schilders, W.H.A.

    2018 57th IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers (IEEE), 2018. blz. 3217-3222.

    Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

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    T1 - A novel Krylov method for model order reduction of quadratic bilinear systems

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    AU - Weiland,S.

    AU - Schilders,W.H.A.

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    N2 - A novel Krylov subspace method is proposed to substantially reduce the computational complexity of the special class of quadratic bilinear dynamical systems. Based on the first two generalized transfer functions of the system, a Petrov-Galerkin projection scheme is applied. It is shown that such a projection amounts to interpolating the transfer functions at specific points which, in fact, is equivalent to constructing the corresponding Krylov subspace. For single-input single-output systems, the relevant Krylov subspace can be readily constructed for the interpolation points. For multi-input multi-output systems, also user-specified directional information is required so that a tangential interpolation can be determined. The method is demonstrated on a model of a nonlinear transmission line that is reduced from 100 to 10 states with a negligible relative error. In a second application the method is applied to the FitzHugh-Nagumo model.

    AB - A novel Krylov subspace method is proposed to substantially reduce the computational complexity of the special class of quadratic bilinear dynamical systems. Based on the first two generalized transfer functions of the system, a Petrov-Galerkin projection scheme is applied. It is shown that such a projection amounts to interpolating the transfer functions at specific points which, in fact, is equivalent to constructing the corresponding Krylov subspace. For single-input single-output systems, the relevant Krylov subspace can be readily constructed for the interpolation points. For multi-input multi-output systems, also user-specified directional information is required so that a tangential interpolation can be determined. The method is demonstrated on a model of a nonlinear transmission line that is reduced from 100 to 10 states with a negligible relative error. In a second application the method is applied to the FitzHugh-Nagumo model.

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    KW - Quadratic-bilinear systems

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    Cao X, Maubach JML, Weiland S, Schilders WHA. A novel Krylov method for model order reduction of quadratic bilinear systems. In 2018 57th IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers (IEEE). 2018. blz. 3217-3222. Beschikbaar vanaf, DOI: 10.1109/CDC.2018.8619575