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.
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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
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Benner, P., Faßbender, H. (2019). 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_142-2
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DOI: https://doi.org/10.1007/978-1-4471-5102-9_142-2
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Latest
Model Order Reduction: Techniques and Tools- Published:
- 09 October 2019
DOI: https://doi.org/10.1007/978-1-4471-5102-9_142-2
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Original
Model Order Reduction: Techniques and Tools- Published:
- 19 April 2014
DOI: https://doi.org/10.1007/978-1-4471-5102-9_142-1