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at - Automatisierungstechnik

Methoden und Anwendungen der Steuerungs-, Regelungs- und Informationstechnik

[AT - Automation Technology: Methods and Applications of Control, Regulation, and Information Technology

Editor-in-Chief: Jumar, Ulrich

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Volume 61, Issue 8


Model Order Reduction by Approximate Balanced Truncation: A Unifying Framework / Modellreduktion durch approximatives Balanciertes Abschneiden: eine vereinigende Formulierung

Dipl.-Ing. Thomas Wolf
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  • Institute of Automatic Control, Technische Universität München, Boltzmannstr. 15, D-85748 Garching bei München
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/ Dipl.-Ing. Heiko K. F. Panzer / Prof. Dr.-Ing. habil. Boris Lohmann
Published Online: 2013-09-05 | DOI: https://doi.org/10.1524/auto.2013.1007


A novel formulation of approximate truncated balanced realization (TBR) is introduced to unify three approaches: two iterative methods for solving the underlying Lyapunov equations - the alternating directions implicit (ADI) iteration and the rational Krylov subspace method (RKSM) - and a two-step procedure that performs a Krylov-based projection and subsequently direct TBR. The framework allows to compare the three methods with respect to solvability, fidelity, numerical effort, stability preservation and global error bounds, which suggests to merge ADI with the two-step procedure


Eine neue Formulierung des approximativen Balancierten Abschneidens vereinheitlicht drei Varianten: zwei iterative Lösungsverfahren der zugrundeliegenden Ljapunow-Gleichungen - Alternating Directions Implicit (ADI) Iteration und Rational Krylov Subspace Method (RKSM) - und ein Zwei-Schritt-Verfahren (ZSV), welches nacheinander eine Krylow-Projektion und Balanciertes Abschneiden durchführt. Die einheitliche Beschreibung ermöglicht den Vergleich hinsichtlich Lösbarkeit, Approximationsgüte, numerischem Aufwand, Stabilitätserhaltung und globaler Fehlerschranken, was eine Fusion von ADI und ZSV empfiehlt

Keywords : Model order reduction; truncated balanced realization; Krylov; ADI

Schlagwörter : Modellordnungsreduktion; balanciertes Abschneiden; Krylov; ADI

About the article

Dipl.-Ing. Thomas Wolf

Dipl.-Ing. Thomas Wolf is a research assistant at the Institute of Automatic Control of the Faculty of Mechanical Engineering at the Technische Universität München. His field of research includes model order reduction of large-scale systems and port-Hamiltonian model representation.

Dipl.-Ing. Heiko K. F. Panzer

Dipl.-Ing. Heiko K. F. Panzer is a research assistant at the Institute of Automatic Control of the Faculty of Mechanical Engineering at the Technische Universität München. His research interest includes model reduction of large-scale systems by Krylov subspace methods and parametric model order reduction by matrix interpolation.

Prof. Dr.-Ing. habil. Boris Lohmann

Prof. Dr.-Ing. habil. Boris Lohmann is Head of the Institute of Automatic Control of the Faculty of Mechanical Engineering at the Technische Universität München. His research activities include model order reduction, nonlinear, robust and optimal control as well as active vibration control.

Published Online: 2013-09-05

Published in Print: 2013-08-01

Citation Information: at - Automatisierungstechnik, Volume 61, Issue 8, Pages 545–556, ISSN (Online) 2196-677X, ISSN (Print) 0178-2312, DOI: https://doi.org/10.1524/auto.2013.1007.

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