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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

7 Citations (Scopus)

4 Downloads (Pure)

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.

Original language	English
Title of host publication	2018 IEEE Conference on Decision and Control, CDC 2018
Publisher	Institute of Electrical and Electronics Engineers
Pages	3217-3222
Number of pages	6
ISBN (Electronic)	9781538613955
DOIs	https://doi.org/10.1109/CDC.2018.8619575
Publication status	Published - 18 Jan 2019
Event	57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: 17 Dec 2018 → 19 Dec 2018 Conference number: 57

Conference

Conference	57th IEEE Conference on Decision and Control, CDC 2018
Abbreviated title	CDC 2018
Country/Territory	United States
City	Miami
Period	17/12/18 → 19/12/18

Keywords

Model order reduction
Krylov methods
Quadratic-bilinear systems

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10.1109/CDC.2018.8619575

Cite this

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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",

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

publisher = "Institute of Electrical and Electronics Engineers",

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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, Institute of Electrical and Electronics Engineers, pp. 3217-3222, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, Florida, United States, 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. p. 3217-3222 8619575.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

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

AU - Cao, X.

AU - Maubach, J.M.L.

AU - Weiland, S.

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N1 - Conference code: 57

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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 by numerical examples.

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.

KW - Model order reduction

KW - Krylov methods

KW - Quadratic-bilinear systems

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M3 - Conference contribution

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EP - 3222

BT - 2018 IEEE Conference on Decision and Control, CDC 2018

PB - Institute of Electrical and Electronics Engineers

T2 - 57th IEEE Conference on Decision and Control, CDC 2018

Y2 - 17 December 2018 through 19 December 2018

ER -

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

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