Abstract
Model order reduction 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 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 equations can be replaced by a much smaller set of analogous equations 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
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Bibliography
Antoulas A (2005) Approximation of large-scale dynamical systems. SIAM, Philadelphia
Benner P (2006) Numerical linear algebra for model reduction in control and simulation. GAMM Mitt 29(2):275–296
Benner P, Stykel T (2017) Model order reduction for differential-algebraic equations: a survey. In: Ilchmann A, Reis T (eds) Surveys in Differential-algebraic Equations IV, Differential-Algebraic Equations Forum. Springer International Publishing, Cham, pp 107–160
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
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
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), 3–5 Mar 2011 at Hammamet. IEEE Publications, p 6
Benner P, Gugercin S, Willcox K (2015) A survey of model reduction methods for parametric systems. SIAM Rev 57(4):483–531
Benner P, Cohen A, Ohlberger M, Willcox K (2017) Model reduction and approximation. Theory and algorithms. SIAM, Philadelphia
Freund R (2003) Model reduction methods based on Krylov subspaces. Acta Num 12:267–319
Glover K (1984) All optimal Hankel-norm approximations of linear multivariable systems and their L∞ norms. Internat J Control 39:1115–1193
Golub G, Van Loan C (2013) Matrix computations, 4th edn. Johns Hopkins University Press, Baltimore
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
Obinata G, Anderson B (2001) Model reduction for control system design. Communications and Control Engineering Series. Springer, London
Ruhe A, Skoogh D (1998) Rational Krylov algorithms for eigenvalue computation and model reduction. In: Applied parallel computing. Large scale scientific and industrial problems. Lecture Notes in Computer Science, vol 1541. Springer, Berlin/Heidelberg, pp 491–502
Schilders W, van der Vorst H, Rommes J (2008) Model order reduction: theory, research aspects and applications. Springer, Berlin/Heidelberg
Varga A (1991) Balancing-free square-root algorithm for computing singular perturbation approximations. In: Proceedings of the 30th IEEE CDC, Brighton, pp 1062–1065
Varga A (1995) Enhanced modal approach for model reduction. Math Model Syst 1(2):91–105
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
Zhou K, Doyle J, Glover K (1996) Robust and optimal control. Prentice Hall, Upper Saddle River
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this entry
Cite this entry
Benner, P., Faßbender, H. (2021). Model Order Reduction: Techniques and Tools. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, Cham. https://doi.org/10.1007/978-3-030-44184-5_142
Download citation
DOI: https://doi.org/10.1007/978-3-030-44184-5_142
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-44183-8
Online ISBN: 978-3-030-44184-5
eBook Packages: Intelligent Technologies and RoboticsReference Module Computer Science and Engineering