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Model Order Reduction: Techniques and Tools

Encyclopedia of Systems and Control

Abstract

Model order reduction (MOR) is here understood as a computational technique to reduce the order of a dynamical system described by a set of ordinary or differential-algebraic equations (ODEs or DAEs) to facilitate or enable its simulation, the design of a controller, or optimization and design of the physical system modeled. It focuses on representing the map from inputs into the system to its outputs, while its dynamics are treated as a black box so that the large-scale set of describing ODEs/DAEs can be replaced by a much smaller set of ODEs/DAEs without sacrificing the accuracy of the input-to-output behavior.

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Bibliography

  • Antoulas A (2005) Approximation of large-scale dynamical systems. SIAM, Philadelphia

    Book  MATH  Google Scholar 

  • Benner P (2006) Numerical linear algebra for model reduction in control and simulation. GAMM Mitt 29(2):275–296

    MATH  MathSciNet  Google Scholar 

  • Benner P, Quintana-Ortí E, Quintana-Ortí G (2000) Balanced truncation model reduction of large-scale dense systems on parallel computers. Math Comput Model Dyn Syst 6:383–405

    Article  MATH  Google Scholar 

  • Benner P, Mehrmann V, Sorensen D (2005) Dimension reduction of large-scale systems. Lecture Notes in Computational Science and Engineering, vol 45. Springer, Berlin/Heidelberg

    Google Scholar 

  • Benner P, Kressner D, Sima V, Varga A (2010) Die SLICOT-Toolboxen für Matlab (The SLICOT-Toolboxes for Matlab) [German]. at-Automatisierungstechnik 58(1):15–25. English version available as SLICOT working note 2009-1, 2009, http://slicot.org/working-notes/

  • Benner P, Hochstenbach M, Kürschner P (2011) Model order reduction of large-scale dynamical systems with Jacobi-Davidson style eigensolvers. In: Proceedings of the International Conference on Communications, Computing and Control Applications (CCCA), March 3-5, 2011 at Hammamet, Tunisia, IEEE Publications (6 pages)

    Google Scholar 

  • Freund R (2003) Model reduction methods based on Krylov subspaces. Acta Numer 12:267–319

    Article  MATH  MathSciNet  Google Scholar 

  • Glover K (1984) All optimal Hankel-norm approximations of linear multivariable systems and their L∞ norms. Internat J Control 39:1115–1193

    Article  MATH  MathSciNet  Google Scholar 

  • Golub G, Van Loan C (2013) Matrix computations, 4th edn. Johns Hopkins University Press, Baltimore

    MATH  Google Scholar 

  • Gugercin S, Antoulas AC, Beattie C (2008) \(\mathcal{H}_{2}\) model reduction for large-scale dynamical systems. SIAM J Matrix Anal Appl 30(2):609–638

    Google Scholar 

  • Obinata G, Anderson B (2001) Model reduction for control system design. Communications and Control Engineering Series. Springer, London

    Book  Google Scholar 

  • Ruhe A, Skoogh D (1998) Rational Krylov algorithms for eigenvalue computation and model reduction. Applied Parallel Computing. Large Scale Scientific and Industrial Problems, Lecture Notes in Computer Science, vol 1541. Springer, Berlin/Heidelberg, pp 491–502

    Google Scholar 

  • Schilders W, van der Vorst H, Rommes J (2008) Model order reduction: theory, research aspects and applications. Springer, Berlin/Heidelberg

    Book  Google Scholar 

  • Varga A (1991) Balancing-free square-root algorithm for computing singular perturbation approximations. In: Proceedings of the 30th IEEE CDC, Brighton, pp 1062–1065

    Google Scholar 

  • Varga A (1995) Enhanced modal approach for model reduction. Math Model Syst 1(2):91–105

    Article  MATH  Google Scholar 

  • Varga A (2001) Model reduction software in the SLICOT library. In: Datta B (ed) Applied and computational control, signals, and circuits. The Kluwer International Series in Engineering and Computer Science, vol 629. Kluwer Academic, Boston, pp 239–282

    Google Scholar 

  • Zhou K, Doyle J, Glover K (1996) Robust and optimal control. Prentice Hall, Upper Saddle River, NJ

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, D-39106, Magdeburg, Germany

    Peter Benner

  2. Institut Computational Mathematics, Technische Universität Braunschweig, Fallersleber-Tor-Wall 23, D-38100, Braunschweig, Germany

    Heike Faßbender

Authors
  1. Peter Benner
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  2. Heike Faßbender
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Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, Massachusetts, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, Minnesota, USA

    Tariq Samad

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© 2013 Springer-Verlag London

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Benner, P., Faßbender, H. (2013). Model Order Reduction: Techniques and Tools. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_142-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_142-1

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  • Publisher Name: Springer, London

  • Online ISBN: 978-1-4471-5102-9

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Chapter history

  1. Latest

    Model Order Reduction: Techniques and Tools
    Published:
    09 October 2019

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_142-2

  2. Original

    Model Order Reduction: Techniques and Tools
    Published:
    19 April 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_142-1

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