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Research Articles

Near-optimal interpolation-based time-limited model order reduction

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Pages 773-783 | Received 01 Sep 2021, Accepted 25 Jan 2023, Published online: 07 Feb 2023

References

  • Antoulas, A. C., Beattie, C. A., & Gugercin, S.. (2010). Interpolatory model reduction of large-scale dynamical systems. In J. Mohammadpour & K. Grigoriadis (Eds.), Efficient Modelling and Control of Large-Scale Systems (pp. 3–58). Springer. https://doi.org/10.1007/978-1-4419-5757-3_1.
  • Antoulas, A. C., Beattie, C. A., & Gugercin, S. (2020). Interpolatory methods for model reduction. SIAM. https://doi.org/10.1137/1.9781611976083
  • Beattie, C.A., & Gugercin, S.(2007, December 12–14). Krylov based minimization for optimal H2 model reduction. Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, LA, USA. pp. 4385–4390. https://doi.org/10.1109/CDC.2007.4434939
  • Beattie, C. A., & Gugercin, S. (2009, December 16–18). A trust region method for optimal H2 model reduction. Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, P.R.China. pp. 5370–5375. https://doi.org/10.1109/CDC.2009.5400605
  • Benner, P., Grivet-Talocia, S., Quarteroni, A., Rozza, G., & Silveria, L. M. (2020a). Model order reduction: Volume 2: Snapshot-based methods and algorithms. De Gruyter. https://doi.org/10.1515/9783110671490
  • Benner, P., Grivet-Talocia, S., Quarteroni, A., Rozza, G., & Silveria, L. M. (2020b). Model order reduction: Volume 3: Applications. De Gruyter. https://doi.org/10.1515/9783110499001
  • Benner, P., Grivet-Talocia, S., Quarteroni, A., Rozza, G., & Silveria, L. M. (2021). Model order reduction: Volume 1: Systems- and data-driven methods and algorithms. De Gruyter. https://doi.org/10.1515/9783110498967
  • Benner, P., Köhler, M., & Saak, J. (2011, December). Sparse-dense Sylvester equations in H2-model order reduction (Tech. Rep. No. MPIMD/11-11). Max Planck Institute. https://csc.mpi-magdeburg.mpg.de/preprints/2011/MPIMD11-11.pdf.
  • Breiten, T., Beattie, C., & Gugercin, S. (2015). Near-optimal frequency-weighted interpolatory model reduction. Systems & Control Letters, 78, 8–18. https://doi.org/10.1016/j.sysconle.2015.01.005
  • Chahlaoui, Y., & Van Dooren, P. (2005). Benchmark examples for model reduction of linear time-invariant dynamical systems. In P. Benner, D. C. Sorensenand & V. Mehrmann (Eds.), Dimension reduction of large-scale systems (Vol. 45, pp. 379–392). Springer. https://doi.org/10.1007/3-540-27909-1_24
  • Duff, I. P., & Kürschner, P. (2021). Numerical computation and new output bounds for time-limited balanced truncation of discrete-time systems. Linear Algebra and Its Applications, 623, 367–397. https://doi.org/10.1016/j.laa.2020.09.029
  • Flagg, G., Beattie, C., & Gugercin, S. (2012). Convergence of the iterative rational Krylov algorithm. Systems & Control Letters, 61(6), 688–691. https://doi.org/10.1016/j.sysconle.2012.03.005
  • Gawronski, W., & Juang, J. (1990). Model reduction in limited time and frequency intervals. International Journal of Systems Science, 21(2), 349–376. https://doi.org/10.1080/00207729008910366
  • Goyal, P., & Redmann, M. (2019). Time-limited H2-optimal model order reduction. Applied Mathematics and Computation, 355, 184–197. https://doi.org/10.1016/j.amc.2019.02.065
  • Gugercin, S., & Antoulas, A. C. (2003, December). A time-limited balanced reduction method. Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii USA. pp. 5250–5253. https://doi.org/10.1109/CDC.2003.1272471
  • Gugercin, S., Antoulas, A. C., & Beattie, C. (2008). H2 model reduction for large-scale linear dynamical systems. SIAM Journal on Matrix Analysis and Applications, 30(2), 609–638. https://doi.org/10.1137/060666123
  • Holmes, P., Lumley, J. L., Berkooz, G., & Rowley, C. W. (2012). Turbulence, coherent structures, dynamical systems and symmetryed (2nd ed.). Cambridge University Press. https://doi.org/10.1017/CBO9780511919701
  • Kürschner, P. (2018). Balanced truncation model order reduction in limited time intervals for large systems. Advances in Computational Mathematics, 44(6), 1821–1844. https://doi.org/10.1007/s10444-018-9608-6
  • Luenberger, D. G. (1997). Optimization by vector space methods. John Wiley & Sons. https://www.wiley.com/en-us/Optimization+by+Vector+Space+Methods-p-9780471181170
  • Redmann, M. (2020, February). An LT2-error bound for time-limited balanced truncation. Systems & Control Letters, 136, 104620. https://doi.org/10.1016/j.sysconle.2019.104620
  • Redmann, M., & Kürschner, P. (2018). An output error bound for time-limited balanced truncation. Systems & Control Letters, 121, 1–6. https://doi.org/10.1016/j.sysconle.2018.08.004
  • Rommes, J., & Martins, N. (2006). Efficient computation of transfer function dominant poles using subspace acceleration. IEEE Transactions on Power Systems, 21(3), 1218–1226. https://doi.org/10.1109/TPWRS.2006.876671
  • Shaker, H. R., & Shaker, F. (2013, June 17–19). Generalized time-limited balanced reduction method. American Control Conference, Washington, DC, USA. pp. 5530–5535. https://doi.org/10.1109/ACC.2013.6580703
  • Sinani, K., & Gugercin, S. (2019). H2(tf) optimality conditions for a finite-time horizon. Automatica, 110, Article 108604. https://doi.org/10.1016/j.automatica.2019.108604
  • Werner, S. W. (2021). Structure-preserving model reduction for mechanical systems [PhD Dissertation]. Department of Mathematics, Otto von Guericke University, Magdeburg, Germany. https://doi.org/10.25673/38617.
  • Wolf, T. (2014). H2 pseudo-optimal model order reduction [Doctoral dissertation]. Technische Universität München. https://mediatum.ub.tum.de/doc/1228083/file.pdf.
  • Xu, Y., & Zeng, T. (2011). Optimal H2 model reduction for large-scale MIMO systems via tangential interpolation. International Journal of Numerical Analysis & Modeling, 8(1), 174–188. http://www.math.ualberta.ca/ijnam/Volume-8-2011/No-1-11/2011-01-10.pdf.
  • Zulfiqar, U., Sreeram, V., & Du, X. (2020). Time-limited pseudo-optimal H2-model order reduction. IET Control Theory & Applications, 14(14), 1995–2007. https://doi.org/10.1049/iet-cta.2019.1105

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