Model order reduction based on low-rank decomposition of the cross Gramian

References

• Aldhaheri, R. W. (1991). Model order reduction via real Schur-form decomposition. International Journal of Control, 53(3), 709–716. https://doi.org/10.1080/00207179108953642
   Web of Science ®Google Scholar
• Amsallem, D., & Farhat, C. (2012). Stabilization of projection-based reduced-order models. International Journal for Numerical Methods in Engineering, 91(4), 358–377. https://doi.org/10.1002/nme.v91.4
   Web of Science ®Google Scholar
• Antoulas, A. C. (2005). Approximation of large-scale dynamical systems. SIAM.
   Google Scholar
• Antoulas, A. C., Beattie, C. A., & Gugercin, S. (2020). Interpolatory methods for model reduction. SIAM.
   Google Scholar
• Antoulas, A. C., Sorensen, D. C., & Serkan, G. (2001). A survey of model reduction methods for large-scale systems. Contemporary Mathematics, 280, 193–219. https://doi.org/10.1090/conm/280
   Google Scholar
• Baur, U., & Benner, P. (2008). Gramian-based model reduction for data-sparse systems. SIAM Journal on Scientific Computing, 31(1), 776–798. https://doi.org/10.1137/070711578
   Web of Science ®Google Scholar
• Benner, P., Gugercin, S., & Willcox, K. (2015). A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Review, 57(4), 483–531. https://doi.org/10.1137/130932715
   Web of Science ®Google Scholar
• Benner, P., & Himpe, C. (2019). Cross-Gramian-based dominant subspaces. Advances in Computational Mathematics, 45(5-6), 2533–2553. https://doi.org/10.1007/s10444-019-09724-7
   Web of Science ®Google Scholar
• Benner, P., Ohlberger, M., Cohen, A., & Willcox, K. (2017). Model reduction and approximation: Theory and algorithms. SIAM.
   Google Scholar
• Benner, P., & Werner, S. W. (2021). MORLAB-The model order reduction laboratory (version 5.0). In Model reduction of complex dynamical systems (pp. 393–415). Springer.
   Google Scholar
• Bond, B. N., & Daniel, L. (2008). Guaranteed stable projection-based model reduction for indefinite and unstable linear systems. In 2008 IEEE/ACM International Conference on Computer-Aided Design (pp. 728–735). IEEE.
   Google Scholar
• De Abreugarcia, J., & Fairman, F. W. (1986). A note on cross Grammians for orthogonally symmetric realizations. IEEE Transactions on Automatic Control, 31(9), 866–868. https://doi.org/10.1109/TAC.1986.1104421
   Web of Science ®Google Scholar
• Fernando, K., & Nicholson, H. (1983). On the structure of balanced and other principal representations of SISO systems. IEEE Transactions on Automatic Control, 28(2), 228–231. https://doi.org/10.1109/TAC.1983.1103195
   Web of Science ®Google Scholar
• Fernando, K., & Nicholson, H. (1985). On the cross-Gramian for symmetric MIMO systems. IEEE Transactions on Circuits and Systems, 32(5), 487–489. https://doi.org/10.1109/TCS.1985.1085737
   Google Scholar
• Gallivan, K. A., Vandendorpe, A., & Van Dooren, P. (2004). Sylvester equations and projection-based model reduction. Journal of Computational and Applied Mathematics, 162(1), 213–229. https://doi.org/10.1016/j.cam.2003.08.026
   Web of Science ®Google Scholar
• Gawronski, W., & Juang, J.-N. (1990). Model reduction in limited time and frequency intervals. International Journal of Systems Science, 21(2), 349–376. https://doi.org/10.1080/00207729008910366
   Web of Science ®Google Scholar
• Gugercin, S., & Antoulas, A. C. (2004). A survey of model reduction by balanced truncation and some new results. International Journal of Control, 77(8), 748–766. https://doi.org/10.1080/00207170410001713448
   Web of Science ®Google Scholar
• Gugercin, S., Sorensen, D. C., & Antoulas, A. C. (2003). A modified low-rank Smith method for large-scale Lyapunov equations. Numerical Algorithms, 32(1), 27–55. https://doi.org/10.1023/A:1022205420182
   Web of Science ®Google Scholar
• Himpe, C., Leibner, T., & Rave, S. (2018). Hierarchical approximate proper orthogonal decomposition. SIAM Journal on Scientific Computing, 40(5), A3267–A3292. https://doi.org/10.1137/16M1085413
   Web of Science ®Google Scholar
• Himpe, C., & Ohlberger, M. (2014). Cross-Gramian-based combined state and parameter reduction for large-scale control systems. Mathematical Problems in Engineering, 2014, 1–13. https://doi.org/10.1155/2014/843869
   Web of Science ®Google Scholar
• Himpe, C., & Ohlberger, M. (2016). A note on the cross Gramian for non-symmetric systems. Systems Science & Control Engineering, 4(1), 199–208. https://doi.org/10.1080/21642583.2016.1215273
   Web of Science ®Google Scholar
• Ionescu, T. C., Astolfi, A., & Colaneri, P. (2014). Families of moment matching based, low order approximations for linear systems. Systems & Control Letters, 64(1), 47–56. https://doi.org/10.1016/j.sysconle.2013.10.011
   Web of Science ®Google Scholar
• Jiang, Y., Qi, Z., & Yang, P. (2019). Model order reduction of linear systems via the cross Gramian and SVD. IEEE Transactions on Circuits and Systems II-Express Briefs, 66(3), 422–426. https://doi.org/10.1109/TCSII.8920
   Web of Science ®Google Scholar
• Jiang, Y., & Xu, K. (2017). H2 optimal reduced models of general MIMO LTI systems via the cross Gramian on the Stiefel manifold. Journal of The Franklin Institute-Engineering and Applied Mathematics, 354(8), 3210–3224. https://doi.org/10.1016/j.jfranklin.2017.02.019
   Web of Science ®Google Scholar
• Jiang, Y.-L. (2010). Model order reduction methods. Science Press.
   Google Scholar
• Jiang, Y.-L., & Chen, H.-B. (2012a). Application of general orthogonal polynomials to fast simulation of nonlinear descriptor systems through piecewise-linear approximation. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 31(5), 804–808. https://doi.org/10.1109/TCAD.2011.2179879
   Web of Science ®Google Scholar
• Jiang, Y.-L., & Chen, H.-B. (2012b). Time domain model order reduction of general orthogonal polynomials for linear input-output systems. IEEE Transactions on Automatic Control, 57(2), 330–343. https://doi.org/10.1109/TAC.2011.2161839
   Web of Science ®Google Scholar
• Kailath, T. (1980). Linear systems. (Vol. 156). Prentice-Hall Englewood Cliffs, NJ.
   Google Scholar
• Kamon, M., Wang, F., & White, J. (2000). Generating nearly optimally compact models from Krylov-subspace based reduced-order models. IEEE Transactions on Circuits and Systems Ii: Analog and Digital Signal Processing, 47(4), 239–248. https://doi.org/10.1109/82.839660
   Google Scholar
• Knockaert, L., & De Zutter, D. (2003). Stable Laguerre-SVD reduced-order modeling. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 50(4), 576–579. https://doi.org/10.1109/TCSI.2003.809807
   Google Scholar
• Korvink, J. G., & Rudnyi, E. B. (2005). Oberwolfach benchmark collection. In Dimension reduction of large-scale systems (pp. 311–315). Springer.
   Google Scholar
• 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
   Web of Science ®Google Scholar
• Laub, A. J., Silverman, L. M., & Verma, M. (1983). A note on cross-Grammians for symmetric realizations. In Proceedings of the IEEE (Vol. 71, pp. 904–905). IEEE.
   Google Scholar
• Li, J.-R., & Kamon, M. (2005). PEEC model of a spiral inductor generated by Fasthenry. In Dimension reduction of large-scale systems (pp. 373–377). Springer.
   Google Scholar
• Li, J.-R., & White, J. (2001). Reduction of large circuit models via low rank approximate Gramians. International Journal of Applied Mathematics and Computer Science, 11(5), 1151–1171.
   Google Scholar
• Lu, K., Jin, Y., Chen, Y., Yang, Y., Hou, L., Zhang, Z., Li, Z., & Fu, C. (2019). Review for order reduction based on proper orthogonal decomposition and outlooks of applications in mechanical systems. Mechanical Systems and Signal Processing, 123(3), 264–297. https://doi.org/10.1016/j.ymssp.2019.01.018
   Web of Science ®Google Scholar
• Megretski, A. (2004). Lecture notes on projection-based model reduction. http://web.mit.edu/6.242/www/syll.html
   Google Scholar
• Montier, L., Henneron, T., Goursaud, B., & Clenet, S. (2017). Balanced proper orthogonal decomposition applied to magnetoquasi-static problems through a stabilization methodology. IEEE Transactions on Magnetics, 53(7), 1–10. https://doi.org/10.1109/TMAG.2017.2683448
   Web of Science ®Google Scholar
• Moore, B. (1981). Principal component analysis in linear systems: Controllability, observability, and model reduction. IEEE Transactions on Automatic Control, 26(1), 17–32. https://doi.org/10.1109/TAC.1981.1102568
   Web of Science ®Google Scholar
• Penzl, T. (2006). Algorithms for model reduction of large dynamical systems. Linear Algebra and Its Applications, 415(2-3), 322–343. https://doi.org/10.1016/j.laa.2006.01.007
   Web of Science ®Google Scholar
• Perev, K. (2015). Cross Gramian approximation with Laguerre polynomials for model order reduction. AIP Conference Proceedings, 1690(1), 020013–1–020013–9. https://doi.org/10.1063/1.4936691
   Google Scholar
• Qi, Z.-Z., Jiang, Y.-L., & Xiao, Z.-H. (2021). Model order reduction based on approximate cross Gramian and Laguerre series for linear input-output systems. IEEE Access, 9, 22328–22338. https://doi.org/10.1109/Access.6287639
   Web of Science ®Google Scholar
• Redmann, M. (2020). An LT2-error bound for time-limited balanced truncation. Systems & Control Letters, 136, 104620. https://doi.org/10.1016/j.sysconle.2019.104620
   Web of Science ®Google Scholar
• 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
   Web of Science ®Google Scholar
• Saad, Y. (2003). Iterative methods for sparse linear systems. SIAM.
   Google Scholar
• Saad, Y., & Schultz, M. H. (1986). GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing, 7(3), 856–869. https://doi.org/10.1137/0907058
   Web of Science ®Google Scholar
• Song, Q., Jiang, Y., & Xiao, Z. (2017). Arnoldi-based model order reduction for linear systems with inhomogeneous initial conditions. Journal of The Franklin Institute-Engineering and Applied Mathematics, 354(18), 8570–8585. https://doi.org/10.1016/j.jfranklin.2017.10.014
   Web of Science ®Google Scholar
• Sorensen, D. C., & Antoulas, A. C. (2002). The Sylvester equation and approximate balanced reduction. Linear Algebra and Its Applications, 351-352, 671–700. https://doi.org/10.1016/S0024-3795(02)00283-5
   Web of Science ®Google Scholar
• Steinbuch, M., Schootstra, G., & Bosgra, O. H. (1992). Robust control of a compact disc player. In Decision and Control, 1992. Proceedings of the 31st IEEE Conference on (pp. 2596–2600). IEEE.
   Google Scholar
• Szego, G. (1939). Orthogonal polynomials. American Mathematical Society.
   Google Scholar
• Varga, A. (1991). Balancing free square-root algorithm for computing singular perturbation approximations. In Proceedings of the 30th IEEE Conference on Decision and Control (pp. 1062–1065). IEEE.
   Google Scholar
• Wang, J. M., Chu, C. C., Yu, Q., & E. S. Kuh (2002). On projection-based algorithms for model-order reduction of interconnects. IEEE Transactions on Circuits and Systems I-regular Papers, 49(11), 1563–1585. https://doi.org/10.1109/TCSI.2002.804542
   Web of Science ®Google Scholar
• Xiang, S. (2012). On error bounds for orthogonal polynomial expansions and gauss-type quadrature. SIAM Journal on Numerical Analysis, 50(3), 1240–1263. https://doi.org/10.1137/110820841
   Web of Science ®Google Scholar
• Xiao, Z., Jiang, Y., & Qi, Z. (2019a). Finite-time balanced truncation for linear systems via shifted Legendre polynomials. Systems & Control Letters, 126, 48–57. https://doi.org/10.1016/j.sysconle.2019.03.004
   Web of Science ®Google Scholar
• Xiao, Z., Jiang, Y., & Qi, Z. (2019b). Structure preserving balanced proper orthogonal decomposition for second-order form systems via shifted Legendre polynomials. IET Control Theory and Applications, 13(8), 1155–1165. https://doi.org/10.1049/cth2.v13.8
   Web of Science ®Google Scholar