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

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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.
LanguageEnglish
Title of host publication2018 57th IEEE Conference on Decision and Control
PublisherInstitute of Electrical and Electronics Engineers
Pages3217-3222
Number of pages6
DOIs
StatePublished - Dec 2018
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: 17 Dec 201819 Dec 2018
Conference number: 57

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
Abbreviated titleCDC 2018
CountryUnited States
CityMiami
Period17/12/1819/12/18

Fingerprint

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

Keywords

  • Model order reduction
  • Krylov methods
  • Quadratic-bilinear systems

Cite this

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 (pp. 3217-3222). Institute of Electrical and Electronics Engineers. 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, 2018. pp. 3217-3222
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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.",
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year = "2018",
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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, pp. 3217-3222, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 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, 2018. p. 3217-3222.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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

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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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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. 2018. p. 3217-3222. Available from, DOI: 10.1109/CDC.2018.8619575