Skip to main content

Model Order Reduction: Techniques and Tools

  • Reference work entry
  • First Online:
Encyclopedia of Systems and Control
  • 317 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 899.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 549.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Bibliography

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

    Google Scholar 

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

    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

    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-Automatisierung-stechnik 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

    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

    MathSciNet  Google Scholar 

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

    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

    MathSciNet  Google Scholar 

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

    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

    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

    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

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag London

About this entry

Cite this entry

Benner, P., Faßbender, H. (2015). Model Order Reduction: Techniques and Tools. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5058-9_142

Download citation

Publish with us

Policies and ethics