Optimal Angle Reduction - A Behavioral Approach to Linear System Approximation

B. Roorda, S. Weiland

Research output: Working paperDiscussion paperOther research output

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Abstract

We investigate the problem of optimal state reduction under minimization of the angle between system behaviors. The angle is defined in a worst-case sense, as the largest angle that can occur between a system trajectory and its optimal approximation in the reduced order model. This problem is analysed for linear time-invariant finite dimensional systems, in a behavioral l2-setting, without reference to input/output decompositions and stability considerations. The notion of a weakest past-future link is introduced and it is shown how this concept is applied for the purpose of model reduction. A method that reduces the state dimension by one is presented and shown to be optimal. Specific algorithms are provided for the numerical implementation of the approximation method.
Original languageEnglish
Place of PublicationTilburg
PublisherFinance
Number of pages34
Volume2000-31
Publication statusPublished - 2000

Publication series

NameCentER Discussion Paper
Volume2000-31

Fingerprint

Linear systems
Trajectories
Decomposition

Keywords

  • Optimal model reduction
  • State space balancing
  • l2-systems
  • Least squares optimization
  • Gap metrics
  • Hankelnorm reduction

Cite this

Roorda, B., & Weiland, S. (2000). Optimal Angle Reduction - A Behavioral Approach to Linear System Approximation. (CentER Discussion Paper; Vol. 2000-31). Tilburg: Finance.
Roorda, B. ; Weiland, S. / Optimal Angle Reduction - A Behavioral Approach to Linear System Approximation. Tilburg : Finance, 2000. (CentER Discussion Paper).
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abstract = "We investigate the problem of optimal state reduction under minimization of the angle between system behaviors. The angle is defined in a worst-case sense, as the largest angle that can occur between a system trajectory and its optimal approximation in the reduced order model. This problem is analysed for linear time-invariant finite dimensional systems, in a behavioral l2-setting, without reference to input/output decompositions and stability considerations. The notion of a weakest past-future link is introduced and it is shown how this concept is applied for the purpose of model reduction. A method that reduces the state dimension by one is presented and shown to be optimal. Specific algorithms are provided for the numerical implementation of the approximation method.",
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Roorda, B & Weiland, S 2000 'Optimal Angle Reduction - A Behavioral Approach to Linear System Approximation' CentER Discussion Paper, vol. 2000-31, Finance, Tilburg.

Optimal Angle Reduction - A Behavioral Approach to Linear System Approximation. / Roorda, B.; Weiland, S.

Tilburg : Finance, 2000. (CentER Discussion Paper; Vol. 2000-31).

Research output: Working paperDiscussion paperOther research output

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T1 - Optimal Angle Reduction - A Behavioral Approach to Linear System Approximation

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AU - Weiland, S.

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N2 - We investigate the problem of optimal state reduction under minimization of the angle between system behaviors. The angle is defined in a worst-case sense, as the largest angle that can occur between a system trajectory and its optimal approximation in the reduced order model. This problem is analysed for linear time-invariant finite dimensional systems, in a behavioral l2-setting, without reference to input/output decompositions and stability considerations. The notion of a weakest past-future link is introduced and it is shown how this concept is applied for the purpose of model reduction. A method that reduces the state dimension by one is presented and shown to be optimal. Specific algorithms are provided for the numerical implementation of the approximation method.

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KW - Least squares optimization

KW - Gap metrics

KW - Hankelnorm reduction

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Roorda B, Weiland S. Optimal Angle Reduction - A Behavioral Approach to Linear System Approximation. Tilburg: Finance. 2000. (CentER Discussion Paper).