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

X. Cao; J.M.L. Maubach; S. Weiland; W.H.A. Schilders

doi:10.1109/CDC.2018.8619575

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

X. Cao, J.M.L. Maubach, S. Weiland, W.H.A. Schilders

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

6 Citaten (Scopus)

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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 by numerical examples.

Originele taal-2	Engels
Titel	2018 IEEE Conference on Decision and Control, CDC 2018
Uitgeverij	Institute of Electrical and Electronics Engineers
Pagina's	3217-3222
Aantal pagina's	6
ISBN van elektronische versie	9781538613955
DOI's	https://doi.org/10.1109/CDC.2018.8619575
Status	Gepubliceerd - 18 jan. 2019
Evenement	57th IEEE Conference on Decision and Control, CDC 2018 - Miami, Verenigde Staten van Amerika Duur: 17 dec. 2018 → 19 dec. 2018 Congresnummer: 57

Publicatie series

Naam	Proceedings of the IEEE Conference on Decision and Control
Volume	2018-December
ISSN van geprinte versie	0743-1546
ISSN van elektronische versie	2576-2370

Congres

Congres	57th IEEE Conference on Decision and Control, CDC 2018
Verkorte titel	CDC 2018
Land/Regio	Verenigde Staten van Amerika
Stad	Miami
Periode	17/12/18 → 19/12/18

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10.1109/CDC.2018.8619575

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Cao, X., Maubach, J. M. L., Weiland, S., & Schilders, W. H. A. (2019). A novel Krylov method for model order reduction of quadratic bilinear systems. In 2018 IEEE Conference on Decision and Control, CDC 2018 (blz. 3217-3222). Article 8619575 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC.2018.8619575

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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 by numerical examples.",

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 = "2019",

month = jan,

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doi = "10.1109/CDC.2018.8619575",

language = "English",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers",

pages = "3217--3222",

booktitle = "2018 IEEE Conference on Decision and Control, CDC 2018",

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note = "57th IEEE Conference on Decision and Control, CDC 2018, CDC 2018 ; Conference date: 17-12-2018 Through 19-12-2018",

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Cao, X, Maubach, JML , Weiland, S & Schilders, WHA 2019, A novel Krylov method for model order reduction of quadratic bilinear systems. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8619575, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers, blz. 3217-3222, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, Florida, Verenigde Staten van Amerika, 17/12/18. https://doi.org/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. et al.
2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers, 2019. blz. 3217-3222 8619575 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

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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 by numerical examples.

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

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