Optimal Hankel Norm Model Reduction by Truncation of Trajectories

B. Roorda, S. Weiland

Research output: Working paperDiscussion paperOther research output

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Abstract

We show how optimal Hankel-norm approximations of dynamical systems allow for a straightforward interpretation in terms of system trajectories. It is shown that for discrete time single-input systems optimal reductions are obtained by cutting 'balanced trajectories', i.e., by disconnecting the past and future in the input-output pairs relating to left- and right singular vectors of the system. A self-contained proof of optimality is given, and formulas are derived in terms of Faddeev sequences. Some parallels with the literature are briefly indicated.
Original languageEnglish
Place of PublicationTilburg
PublisherFinance
Number of pages6
Volume2000-30
Publication statusPublished - 2000

Publication series

NameCentER Discussion Paper
Volume2000-30

Fingerprint

Hankel
Model Reduction
Truncation
Trajectory
Norm
Singular Vectors
Optimal System
Optimality
Discrete-time
Dynamical system
Output
Approximation
Interpretation

Keywords

  • Optimal Hankel norm approximation
  • Balancing
  • Linear systems
  • l2-systems
  • Faddeev sequences

Cite this

Roorda, B., & Weiland, S. (2000). Optimal Hankel Norm Model Reduction by Truncation of Trajectories. (CentER Discussion Paper; Vol. 2000-30). Tilburg: Finance.
Roorda, B. ; Weiland, S. / Optimal Hankel Norm Model Reduction by Truncation of Trajectories. Tilburg : Finance, 2000. (CentER Discussion Paper).
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Roorda, B & Weiland, S 2000 'Optimal Hankel Norm Model Reduction by Truncation of Trajectories' CentER Discussion Paper, vol. 2000-30, Finance, Tilburg.

Optimal Hankel Norm Model Reduction by Truncation of Trajectories. / Roorda, B.; Weiland, S.

Tilburg : Finance, 2000. (CentER Discussion Paper; Vol. 2000-30).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Optimal Hankel Norm Model Reduction by Truncation of Trajectories

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AU - Weiland, S.

N1 - Pagination: 6

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N2 - We show how optimal Hankel-norm approximations of dynamical systems allow for a straightforward interpretation in terms of system trajectories. It is shown that for discrete time single-input systems optimal reductions are obtained by cutting 'balanced trajectories', i.e., by disconnecting the past and future in the input-output pairs relating to left- and right singular vectors of the system. A self-contained proof of optimality is given, and formulas are derived in terms of Faddeev sequences. Some parallels with the literature are briefly indicated.

AB - We show how optimal Hankel-norm approximations of dynamical systems allow for a straightforward interpretation in terms of system trajectories. It is shown that for discrete time single-input systems optimal reductions are obtained by cutting 'balanced trajectories', i.e., by disconnecting the past and future in the input-output pairs relating to left- and right singular vectors of the system. A self-contained proof of optimality is given, and formulas are derived in terms of Faddeev sequences. Some parallels with the literature are briefly indicated.

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KW - Balancing

KW - Linear systems

KW - l2-systems

KW - Faddeev sequences

M3 - Discussion paper

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T3 - CentER Discussion Paper

BT - Optimal Hankel Norm Model Reduction by Truncation of Trajectories

PB - Finance

CY - Tilburg

ER -

Roorda B, Weiland S. Optimal Hankel Norm Model Reduction by Truncation of Trajectories. Tilburg: Finance. 2000. (CentER Discussion Paper).