Tangential interpolation-based eigensystem realization algorithm for MIMO systems

References

• I. Houtzager, J. Van Wingerden, and M. Verhaegen, Recursive predictor-based subspace identification with application to the real-time closed-loop tracking of flutter, IEEE Trans. Control Syst. Technol. 20 (2012), pp. 934–949. doi:10.1109/TCST.2011.2157694
   Web of Science ®Google Scholar
• D.C. Rebolho, E.M. Belo, and F.D. Marques, Aeroelastic parameter identification in wind tunnel testing via the extended eigensystem realization algorithm, J. Vib. Control 20 (2014), pp. 1607–1621. doi:10.1177/1077546312474015
   Web of Science ®Google Scholar
• M. Döhler and L. Mevel, Fast multi-order computation of system matrices in subspace-based system identification, Control Eng. Pract. 20 (2012), pp. 882–894. doi:10.1016/j.conengprac.2012.05.005
   Web of Science ®Google Scholar
• J.M. Caicedo, S. Dyke, and E. Johnson, Natural excitation technique and eigensystem realization algorithm for phase I of the IASC-ASCE benchmark problem: Simulated data, J. Eng. Mech. 130 (2004), pp. 49–60. doi:10.1061/(ASCE)0733-9399(2004)130:1(49)
   Web of Science ®Google Scholar
• J. Borggaard, E. Cliff, and S. Gugercin, Model reduction for indoor-air behavior in control design for energy-efficient buildings, Proceedings of the American Control Conference, Montreal, 2012, pp. 2283–2288. ISBN 9781457710957
   Google Scholar
• Z. Ma, S. Ahuja, and C. Rowley, Reduced-order models for control of fluids using the eigensystem realization algorithm, Theor. Comput. Fluid Dyn. 25 (2011), pp. 233–247. doi:10.1007/s00162-010-0184-8
   Web of Science ®Google Scholar
• F. Juillet, P. Schmid, and P. Huerre, Control of amplifier flows using subspace identification techniques, J. Fluid. Mech. 725 (2013), pp. 522–565. doi:10.1017/jfm.2013.194
   Web of Science ®Google Scholar
• C. Wales, A. Gaitonde, and D. Jones, Stabilisation of reduced order models via restarting, Int. J. Numer. Methods Fluids 73 (2013), pp. 578–599. doi:10.1002/fld.v73.6
   Web of Science ®Google Scholar
• J. Mendel, Minimum-variance deconvolution, IEEE Trans. Geosci. Remote Sensing GE-19 (1981), pp. 161–171. doi:10.1109/TGRS.1981.350346
   Web of Science ®Google Scholar
• M. Viberg, Subspace-based methods for the identification of linear time-invariant systems, Automatica 31 (1995), pp. 1835–1851. doi:10.1016/0005-1098(95)00107-5
   Web of Science ®Google Scholar
• S. Qin, An overview of subspace identification, Comput. Chem. Eng. 30 (2006), pp. 1502–1513. doi:10.1016/j.compchemeng.2006.05.045
   Web of Science ®Google Scholar
• E. Reynders, System identification methods for (operational) modal analysis: Review and comparison, Arch. Comput. Methods Eng. 19 (2012), pp. 51–124. doi:10.1007/s11831-012-9069-x
   Web of Science ®Google Scholar
• S.Y. Kung, A new identification and model reduction algorithm via singular value decomposition, Proceedings of 12th Asilomar Conference on Circuits, Systems & Computers, Pacific Grove, CA, 1978, pp. 705–714. IEEE.
   Google Scholar
• J.-N. Juang and R. Pappa, An eigensystem realization algorithm for modal parameter identification and model reduction, J. Guidance, Control, Dyn. 8 (1985), pp. 620–627. doi:10.2514/3.20031
   Web of Science ®Google Scholar
• G. Pitstick, J. Cruz, and R. Mulholland, Approximate realization algorithms for truncated impulse response data, IEEE Trans. Acoust. Speech Signal Process. 34 (1986), pp. 1583–1588. doi:10.1109/TASSP.1986.1164997
   Google Scholar
• R. Longman and J.-N. Juang, Recursive form of the eigensystem realization algorithm for system identification, J. Guidance, Control, Dyn. 12 (1989), pp. 647–652. doi:10.2514/3.20458
   Web of Science ®Google Scholar
• J. Singler, Model reduction of linear PDE systems: A continuous time eigensystem realization algorithm, Proceedings of the American Control Conference, Montreal, 2012, pp. 1424–1429.
   Google Scholar
• K. Willcox and J. Peraire, Balanced model reduction via the proper orthogonal decomposition, AIAA J. 40 (2002), pp. 2323–2330. doi:10.2514/2.1570
   Google Scholar
• C. Rowley, Model reduction for fluids, using balanced proper orthogonal decomposition, Int. J. Bifur. Chaos 15 (2005), pp. 997–1013. doi:10.1142/S0218127405012429
   Web of Science ®Google Scholar
• D. Yu and S. Chakravorty, A randomized proper orthogonal decomposition technique, arXiv preprint arXiv:1312.3976, 2013.
   Google Scholar
• A.C. Antoulas, Approximation of Large-Scale Dynamical Systems, Advances in Design and Control Society for Industrial and Applied Mathematics, Philadelphia, PA, 2005.
   Google Scholar
• U. Baur, P. Benner, and L. Feng, Model order reduction for linear and nonlinear systems: A system-theoretic perspective, Arch. Comput. Methods Eng. 21 (2014), pp. 331–358. doi:10.1007/s11831-014-9111-2
   Web of Science ®Google Scholar
• A.C. Antoulas, C.A. Beattie, and S. Gugercin, Interpolatory model reduction of large-scale dynamical systems, in Efficient Modeling and Control of Large-Scale Systems, J. Mohammadpour and M.K. Grigoriadis, eds., Springer US, Boston, MA, 2010, pp. 3–58.
   Google Scholar
• B. Moore, Principal component analysis in linear systems: Controllability, observability, and model reduction, IEEE Trans. Automat. Contr. 26 (1981), pp. 17–32. doi:10.1109/TAC.1981.1102568
   Web of Science ®Google Scholar
• C. Mullis and R. Roberts, Synthesis of minimum roundoff noise fixed point digital filters, IEEE Trans. Circuits Syst. 23 (1976), pp. 551–562. doi:10.1109/TCS.1976.1084254
   Google Scholar
• S. Gugercin, A. Antoulas, and C.A. Beattie, model reduction for large-scale linear dynamical systems, SIAM J. Matrix Anal. Appl. 30 (2008), pp. 609–638. doi:10.1137/060666123
   Web of Science ®Google Scholar
• K. Glover, All optimal Hankel-norm approximations of linear multivariable systems and their L,∞-error bounds, Int. J. Control 39 (1984), pp. 1115–1193. doi:10.1080/00207178408933239
   Web of Science ®Google Scholar
• A. Mayo and A. Antoulas, A framework for the solution of the generalized realization problem, Linear Algebra Appl. 425 (2007), pp. 634–662. doi:10.1016/j.laa.2007.03.008
   Web of Science ®Google Scholar
• B. Gustavsen and A. Semlyen, Rational approximation of frequency domain responses by vector fitting, IEEE Trans. Power Deliv. 14 (1999), pp. 1052–1061. doi:10.1109/61.772353
   Web of Science ®Google Scholar
• Z. Drmač, S. Gugercin, and C. Beattie, Quadrature-based vector fitting for discretized approximation, SIAM J. Sci. Comput. 37 (2015), pp. A625–A652. doi:10.1137/140961511
   Web of Science ®Google Scholar
• C. Beattie and S. Gugercin, Realization–independent approximation, Proceedings of the 51st IEEE Conference on Decision & Control, Maui, HI, IEEE, 2012, pp. 4953–4958.
   Google Scholar
• C. Sanathanan and J. Koerner, Transfer function synthesis as a ratio of two complex polynomials, IEEE Trans. Autom. Control 8 (1963), pp. 56–58. doi:10.1109/TAC.1963.1105517
   Web of Science ®Google Scholar
• M. Berljafa and S. Güttel, Generalized rational Krylov decompositions with an application to rational approximation, SIAM J. Matrix Anal. Appl. 36 (2015), pp. 894–916. doi:10.1137/140998081
   Web of Science ®Google Scholar
• Z. Drmač, S. Gugercin, and C. Beattie, Vector fitting for matrix-valued rational approximation, SIAM J. Scientific Comput. 37 (2015), pp. A2346–A2379. doi:10.1137/15M1010774
   Web of Science ®Google Scholar
• L.M. Silverman, Realization of linear dynamical systems, IEEE Trans. Automat. Contr. 16 (1971), pp. 554–567. doi:10.1109/TAC.1971.1099821
   Web of Science ®Google Scholar
• G. Golub and C.F. Van Loan, Matrix Computations, Johns Hopkins University, Press, Baltimore, MD, 1996, pp. 374–426.
   Google Scholar
• C.A. Beattie and S. Gugercin, Model reduction by rational interpolation, in Model Reduction and Approximation for Complex Systems, P. Benner, A. Cohen, M. Ohlberger, and K. Willcox, eds., Marseille, 2014. Available at http://arxiv.org/abs/1409.2140.
   Google Scholar
• P. Feldmann and F. Liu, Sparse and efficient reduced order modeling of linear subcircuits with large number of terminals, in IEEE/ACM International Conference on Computer Aided Design, 2004. ICCAD-2004, 2004, pp. 88–92.
   Google Scholar
• P. Liu, S.X. Tan, B. Yan, and B. McGaughy, An extended SVD-based terminal and model order reduction algorithm, Proceedings of the 2006 IEEE International Behavioral Modeling and Simulation Workshop San Jose, CA, 2006, pp. 44–49.
   Google Scholar
• P. Benner and A. Schneider, Model reduction for linear descriptor systems with many ports, in Progress in Industrial Mathematics at ECMI 2010, M. Günther, A. Bartel, M. Brunk, S. Schöps, M. Striebel, eds., Springer, Berlin, 2012, pp. 137–143.
   Google Scholar
• U. Al-Saggaf and G. Franklin, Model reduction via balanced realizations: An extension and frequency weighting techniques, IEEE Trans. Automat. Contr. 33 (1988), pp. 687–692. doi:10.1109/9.1280
   Web of Science ®Google Scholar
• S. Gugercin, R. Polyuga, C. Beattie, and A. Van Der Schaft, Structure-preserving tangential interpolation for model reduction of port-Hamiltonian systems, Automatica 48 (2012), pp. 1963–1974. doi:10.1016/j.automatica.2012.05.052
   Web of Science ®Google Scholar
• IMTEK - Simulation, Oberwolfach benchmark collection, 2003. Available at http://www.simulation.uni-freiburg.de/downloads/benchmark.
   Google Scholar
• A. Unger and F. Tröltzsch, Fast solution of optimal control problems in the selective cooling of steel, ZAMM Z. Angew. Math. Mech. 81 (2001), pp. 447–456. doi:10.1002/(ISSN)1521-4001
   Web of Science ®Google Scholar
• P. Benner and A. Schneider, Balanced truncation for descriptor systems with many terminals, Max Planck Institute Magdeburg Preprint MPIMD/13-17, 2013. Available at http://www2.mpi-magdeburg.mpg.de/preprints/2013/MPIMD13-17.pdf.
   Google Scholar