Interconnection-based model order reduction – a survey. (English) Zbl 1532.93027
Summary: In this survey we present in an organic, complete, and accessible style the interconnection framework for model order reduction. While this framework originally started as a revisitation of the moment matching method, in the last 15 years it has expanded to provide solutions to the model order reduction problem for general classes of systems, such as nonlinear, time-delay, stochastic, and hybrid, and to give insight on topics as diverse as circuit analysis and optimal control. The main theme of the paper is the characterization of “interconnection behaviors” as primary properties to be maintained by the reduction process. The survey is enriched by historical notes on the development of the interconnection framework.
MSC:
| 93B11 | System structure simplification |
| 93B70 | Networked control |
| 93C10 | Nonlinear systems in control theory |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93E03 | Stochastic systems in control theory (general) |
| 93-02 | Research exposition (monographs, survey articles) pertaining to systems and control theory |
Keywords:
model reduction; nonlinear model reduction; data-driven model reduction; non-intrusive model reduction; time-delay systems; stochastic systemsReferences:
| [1] | Achar, R.; Nakhla, M. S., Simulation of high-speed interconnects. Proceedings of the IEEE, 5, 693-728 (2001) |
| [2] | Adamjan, V. M.; Arov, D. Z.; Krein, M. G., Analytic properties of Schmidt pairs for a Hankel operator and the generalized Schur-Takagi problem. Mathematics of the USSR Sbornik, 31-73 (1971) · Zbl 0248.47019 |
| [3] | Al-Amer, S. H., & Al-Sunni, F. M. (2000). Approximation of time-delay systems. In Proceedings of the 2000 American control conference |
| [4] | Al-Baiyat, S. A.; Bettayeb, M.; Al-Saggaf, U. M., New model reduction scheme for bilinear systems. International Journal of Systems Science, 10, 1631-1642 (1994) · Zbl 0810.93008 |
| [5] | Aldhaheri, R. W., Model order reduction via real Schur-form decomposition. International Journal of Control, 3, 709-716 (1991) · Zbl 0725.93015 |
| [6] | Antoulas, A. C., Approximation of large-scale dynamical systems (2005), SIAM Advances in Design and Control: SIAM Advances in Design and Control Philadelphia, PA · Zbl 1112.93002 |
| [7] | Antoulas, A. C.; Ball, J. A.; Kang, J.; Willems, J. C., On the solution of the minimal rational interpolation problem. Linear Algebra and Its Applications, Special Issue on Matrix Problems, 511-573 (1990) · Zbl 0715.93020 |
| [8] | Antoulas, A. C.; Beattie, C. A.; Gugercin, S. |
| [9] | Antoulas, A. C.; Gosea, I. V.; Ionita, A. C., Model reduction of bilinear systems in the Loewner framework. SIAM Journal on Scientific Computing, 5, B889-B916 (2016) · Zbl 1515.35038 |
| [10] | Antoulas, A. C.; Lefteriu, S., A tutorial introduction to the Loewner framework for model reduction. Model Reduction and Approximation: Theory and Algorithms, 335 (2017) |
| [11] | Antoulas, A. C.; Sorensen, D. C.; Gugercin, S., A survey of model reduction methods for large-scale systems. Contemporary Mathematics, 193-219 (2001) · Zbl 1048.93014 |
| [12] | Artstein, Z., Linear systems with delayed controls: A reduction. IEEE Transactions on Automatic Control, 4, 869-879 (1982) · Zbl 0486.93011 |
| [13] | Astolfi, A. (2007a). Model reduction by moment matching. In IFAC proceedings volumes - 7th IFAC symposium on nonlinear control systems, vol. 40, no. 12 |
| [14] | Astolfi, A. (2007b). A new look at model reduction by moment matching for linear systems. In Proceedings of the 46th IEEE conference on decision and control |
| [15] | Astolfi, A. (2008). Model reduction by moment matching for nonlinear systems. In Proceedings of the 47th IEEE conference on decision and control |
| [16] | Astolfi, A., Model reduction by moment matching for linear and nonlinear systems. IEEE Transactions on Automatic Control, 10, 2321-2336 (2010) · Zbl 1368.93069 |
| [17] | Astolfi, A. (2010b). Model reduction by moment matching, steady-state response and projections. In Proceedings of the 49th IEEE conference on decision and control |
| [18] | Astolfi, A. (2010c). A note on model reduction by moment matching for nonlinear systems. In IFAC proceedings volumes - 8th IFAC symposium on nonlinear control systems, vol. 43, no. 14 |
| [19] | Astolfi, A., Scarciotti, G., Simard, J. D., Faedo, N., & Ringwood, J. V. (2020). Model Reduction by Moment Matching: Beyond Linearity - A Review of the Last 10 Years. In Proceedings of the 59th IEEE conference on decision and control |
| [20] | Astrid, P.; Weiland, S.; Willcox, K.; Backx, T., Missing point estimation in models described by proper orthogonal decomposition. IEEE Transactions on Automatic Control, 10, 2237-2251 (2008) · Zbl 1367.93110 |
| [21] | Bai, Z.; Freund, R. W., A partial Padé-via-Lanczos method for reduced-order modeling. Linear Algebra and its Applications, 139-164 (2001) · Zbl 0980.93012 |
| [22] | Bai, H., Mao, J., & Scarciotti, G. (2023). Model Reduction for Quadratic-Bilinear Time-Delay Systems Using Nonlinear Moments. In IFAC-papersonline - 12th IFAC symposium on nonlinear control systems, vol. 56, no. 1 |
| [23] | Bai, H., Mylvaganam, T., & Scarciotti, G. (2022). Model reduction for quadratic-bilinear systems using nonlinear moments. In Proceedings of the 20th European control conference |
| [24] | Bai, H., & Scarciotti, G. (2024). Two-sided Moment Matching for Quadratic-Bilinear Systems Using Nonlinear Moments. In Proceedings of the 7th IFAC conference on analysis and control of nonlinear dynamics and chaos |
| [25] | Baur, U.; Benner, P., Cross-Gramian based model reduction for data-sparse systems. Electronic Transactions on Numerical Analysis, 256-270, 27 (2008) · Zbl 1170.93315 |
| [26] | Beattie, C. A., & Gugercin, S. (2008). Interpolation Theory for Structure-Preserving Model Reduction. In Proceedings of the 47th IEEE conference on decision and control |
| [27] | Benner, P., Solving large-scale control problems. IEEE Control Systems, 1, 44-59 (2004) |
| [28] | Benner, P.; Breiten, T., Two-sided projection methods for nonlinear model order reduction. SIAM Journal on Scientific Computing, 2, B239-B260 (2015) · Zbl 1312.93016 |
| [29] | Benner, P., Quintana-Ortí, E. S., & Quintana-Ortí, G. (2000). Singular perturbation approximation of large, dense linear systems. In Proceedings of the IEEE international symposium on computer-aided control system design |
| [30] | Benner, P.; Quintana-Ortí, E. S.; Quintana-Ortí, G., Efficient numerical algorithms for balanced stochastic truncation. Applied Mathematics and Computer Science, 5, 1123-1150 (2001) · Zbl 1008.93014 |
| [31] | Benner, P.; Quintana-Ortí, E. S.; Quintana-Ortí, G., State-space truncation methods for parallel model reduction of large-scale systems. Parallel Computing, 11, 1701-1722 (2003) |
| [32] | Benner, P., Quintana-Ortí, E. S., & Quintana-Ortí, G. (2004). Computing optimal Hankel norm approximations of large-scale systems. In Proceedings of the 43rd IEEE conference on decision and control, vol. 3 |
| [33] | Blondel, V. D.; Megretski, A., Unsolved problems in mathematical systems and control theory (2004), Princeton University Press · Zbl 1052.93002 |
| [34] | Breschi, V., Formentin, S., Scarciotti, G., & Astolfi, A. (2019). Simulation-driven fixed-order controller tuning via moment matching. In Proceedings of the 18th European control conference |
| [35] | Bunse-Gerstner, A.; Kubalińska, D.; Vossen, G.; Wilczek, D., \( \mathcal{H}_2\)-Norm optimal model reduction for large scale discrete dynamical MIMO systems. Journal of Computational and Applied Mathematics, 5, 1202-1216 (2010) · Zbl 1178.93032 |
| [36] | Byrnes, C. I.; Lindquist, A.; Georgiou, T. T., A generalized entropy criterion for Nevanlinna-Pick interpolation with degree constraint. IEEE Transactions on Automatic Control, 822-839 (2001) · Zbl 1007.93013 |
| [37] | Byrnes, C. I.; Lindquist, A.; Gusev, S. V.; Matveev, A. S., A complete parameterization of all positive rational extensions of a covariance sequence. IEEE Transactions on Automatic Control, 1841-1857 (1995) · Zbl 0847.93008 |
| [38] | Chen, Y., Model order reduction for nonlinear systems (1999), Massachusetts Institute of Technology, (Ph.D. thesis) |
| [39] | Chiprout, E.; Nakhla, M. S., Analysis of interconnect networks using complex frequency hopping (CFH). IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2, 186-200 (1995) |
| [40] | Chu, C. C.; Lai, M. H.; Feng, W. S., MIMO interconnects order reductions by using the multiple point adaptive-order rational global Arnoldi algorithm. IEICE Transactions on Electronics, 6, 792-802 (2006) |
| [41] | Enns, D. F. (1984). Model reduction with balanced realizations: An error bound and a frequency weighted generalization. In Proceedings of the 23rd IEEE conference on decision and control |
| [42] | Faedo, N., García-Violini, D., Scarciotti, G., Astolfi, A., & Ringwood, J. V. (2019). Robust Moment-Based Energy-Maximising Optimal Control of Wave Energy Converters. In Proceedings of the 58th IEEE conference on decision and control |
| [43] | Faedo, N.; Scarciotti, G.; Astolfi, A.; Ringwood, J. V., Energy-maximising control of wave energy converters using a moment-domain representation. Control Engineering Practice, 85-96 (2018) |
| [44] | Faedo, N., Scarciotti, G., Astolfi, A., & Ringwood, J. V. (2019). Moment-based constrained optimal control of an array of wave energy converters. In Proceedings of the 2019 American control conference |
| [45] | Faedo, N.; Scarciotti, G.; Astolfi, A.; Ringwood, J. V., Energy-maximising moment-based constrained optimal control of ocean wave energy farms. IET Renewable Power Generation, 14, 3395-3408 (2021) |
| [46] | Faedo, N.; Scarciotti, G.; Astolfi, A.; Ringwood, J. V., Nonlinear energy-maximizing optimal control of wave energy systems: A moment-based approach. IEEE Transactions on Control Systems Technology, 6, 2533-2547 (2021) |
| [47] | Faedo, N.; Scarciotti, G.; Astolfi, A.; Ringwood, J. V., On the approximation of moments for nonlinear systems. IEEE Transactions on Automatic Control, 11, 5538-5545 (2021) · Zbl 1536.93109 |
| [48] | Feldmann, P.; Freund, R. W., Efficient linear circuit analysis by Pade approximation via the Lanczos process. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 5, 639-649 (1995) |
| [49] | Fernando, K.; Nicholson, H., On the structure of balanced and other principal representations of SISO systems. IEEE Transactions on Automatic Control, 2, 228-231 (1983) · Zbl 0507.93021 |
| [50] | Fernando, K.; Nicholson, H., On a fundamental property of the cross-Gramian matrix. IEEE Transactions on Circuits and Systems, 5, 504-505 (1984) · Zbl 0538.93008 |
| [51] | Flagg, G.; Beattie, C. A.; Gugercin, S., Interpolatory \(\mathcal{H}_\infty\) model reduction. Systems & Control Letters, 7, 567-574 (2013) · Zbl 1277.93020 |
| [52] | Freund, R. W. (2004). SPRIM: structure-preserving reduced-order interconnect macromodeling. In IEEE/ACM international conference on computer aided design |
| [53] | Fujimoto, K., Balanced realization and model order reduction for port-Hamiltonian systems. Journal of System Design and Dynamics, 3, 694-702 (2008) |
| [54] | Fujimoto, K.; Scherpen, J. M.A., Nonlinear input-normal realizations based on the differential eigenstructure of Hankel operators. IEEE Transactions on Automatic Control, 1, 2-18 (2005) · Zbl 1365.93082 |
| [55] | Fujimoto, K.; Scherpen, J. M.A., Balanced realization and model order reduction for nonlinear systems based on singular value analysis. SIAM Journal on Control and Optimization, 7, 4591-4623 (2010) · Zbl 1213.93025 |
| [56] | Fujimoto, K.; Tsubakino, D., Computation of nonlinear balanced realization and model reduction based on taylor series expansion. Systems & Control Letters, 4, 283-289 (2008) · Zbl 1134.93012 |
| [57] | Galeani, S., & Sassano, M. (2015). Model reduction by moment matching at discontinuous signals via hybrid output regulation. In Proceedings of the 2015 European control conference |
| [58] | Gallivan, K. A.; Grimme, E.; Van Dooren, P., Asymptotic waveform evaluation via a Lanczos method. Applied Mathematics Letters, 5, 75-80 (1994) · Zbl 0810.65067 |
| [59] | Gallivan, K. A.; Vandendorpe, A.; Van Dooren, P., Model reduction of MIMO systems via tangential interpolation. SIAM Journal on Matrix Analysis and Applications, 2, 328-349 (2004) · Zbl 1078.41016 |
| [60] | Gallivan, K. A.; Vandendorpe, A.; Van Dooren, P., Sylvester equations and projection-based model reduction. Journal of Computational and Applied Mathematics, 1, 213-229 (2004) · Zbl 1044.65054 |
| [61] | Gallivan, K. A., Vandendorpe, A., & Van Dooren, P. (2006). Model reduction and the solution of Sylvester equations. In 17th International symposium on mathematical theory of networks and systems |
| [62] | Gawronski, W.; Juang, J. N., Model reduction in limited time and frequency intervals. International Journal of Systems Science, 2, 349-376 (1990) · Zbl 0692.93007 |
| [63] | Georgiou, T. T., Partial realization of covariance sequences (1983), University of Florida, (Ph.D. thesis) |
| [64] | Georgiou, T. T., The interpolation problem with a degree constraint. IEEE Transactions on Automatic Control, 631-635 (1999) · Zbl 1056.93561 |
| [65] | Glover, K., All optimal Hankel-norm approximations of linear multivariable systems and their L \({}^\infty \)-error bounds. International Journal of Control, 6, 1115-1193 (1984) · Zbl 0543.93036 |
| [66] | Glover, K.; Lam, J.; Partington, J. R., Rational approximation of a class of infinite dimensional systems I: Singular value of Hankel operator. Mathematics of Control, Signals, and Systems, 325-344 (1990) · Zbl 0727.41020 |
| [67] | Gong, Z.; Mao, J.; Junyent-Ferre, A.; Scarciotti, G., Model order reduction of large-scale wind farms: A data-driven approach (2024), (submitted for publication) |
| [68] | Gosea, I. V.; Antoulas, A. C., Data-driven model order reduction of quadratic-bilinear systems. Numerical Linear Algebra with Applications, 6 (2018) · Zbl 1513.93013 |
| [69] | Gray, W. S., & Mesko, J. (1997). General Input Balancing and Model Reduction for Linear and Nonlinear Systems. In Proceedings of the 1997 European control conference |
| [70] | Gray, W. S., & Scherpen, J. M. A. (2001). Nonlinear Hilbert adjoints: properties and applications to Hankel singular value analysis. In Proceedings of the 2001 American control conference, vol. 5 |
| [71] | Gray, W. S.; Verriest, E. I., Balanced realizations near stable invariant manifolds. Automatica, 4, 653-659 (2006) · Zbl 1110.93025 |
| [72] | Grepl, M. A.; Maday, Y.; Nguyen, N. C.; Patera, A. T., Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations. ESAIM. Mathematical Modelling and Numerical Analysis, 3, 575-605 (2007) · Zbl 1142.65078 |
| [73] | Grimme, E. J., Krylov projection methods for model reduction (1997), University of Illinois at Urbana-Champaign, (Ph.D. thesis) |
| [74] | Grimme, E. J.; Sorensen, D.; van Dooren, P., Model reduction of state space systems via an implicitly restarted Lanczos method. Numerical Algorithms, 1-31 (1995) · Zbl 0870.65052 |
| [75] | Gu, C. (2009). QLMOR: A new projection-based approach for nonlinear model order reduction. In IEEE/ACM international conference on computer-aided design |
| [76] | Gu, C., QLMOR: A projection-based nonlinear model order reduction approach using quadratic-linear representation of nonlinear systems. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 9, 1307-1320 (2011) |
| [77] | Gugercin, S.; Antoulas, A. C., A survey of model reduction by balanced truncation and some new results. International Journal of Control, 8, 748-766 (2004) · Zbl 1061.93022 |
| [78] | Gugercin, S.; Antoulas, A. C.; Beattie, C., \( \mathcal{H}_2\) Model reduction for large-scale linear dynamical systems. SIAM Journal on Matrix Analysis and Applications, 2, 609-638 (2008) · Zbl 1159.93318 |
| [79] | Gugercin, S.; Li, J. R., Smith-type methods for balanced truncation of large sparse systems, 49-82 · Zbl 1215.93026 |
| [80] | Gugercin, S.; Polyuga, R. V.; Beattie, C.; Van der Schaft, A., Structure-preserving tangential interpolation for model reduction of port-Hamiltonian systems. Automatica, 9, 1963-1974 (2012) · Zbl 1257.93021 |
| [81] | Hinze, M.; Volkwein, S., Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: Error estimates and suboptimal control, 261-306 · Zbl 1079.65533 |
| [82] | Ionescu, T. C., Two-sided time-domain moment matching for linear systems. IEEE Transactions on Automatic Control, 9, 2632-2637 (2016) · Zbl 1359.93079 |
| [83] | Ionescu, T. C., & Astolfi, A. (2010). On moment matching with preservation of passivity and stability. In Proceedings of the 49th IEEE conference on decision and control |
| [84] | Ionescu, T., & Astolfi, A. (2011). Moment matching for linear systems – overview and new results. In IFAC proceedings volumes - 18th IFAC world congress, vol. 44, no. 1 |
| [85] | Ionescu, T. C.; Astolfi, A., Families of moment matching based, structure preserving approximations for linear port Hamiltonian systems. Automatica, 2424-2434 (2013) · Zbl 1364.93113 |
| [86] | Ionescu, T. C., & Astolfi, A. (2013b). Families of reduced order models that achieve nonlinear moment matching. In Proceedings of the 2013 American control conference |
| [87] | Ionescu, T. C., & Astolfi, A. (2013c). Moment matching based controller reduction for linear systems. In 52nd IEEE conference on decision and control |
| [88] | Ionescu, T. C.; Astolfi, A., Nonlinear moment matching-based model order reduction. IEEE Transactions on Automatic Control, 10, 2837-2847 (2016) · Zbl 1359.93080 |
| [89] | Ionescu, T. C.; Astolfi, A.; Colaneri, P., Families of moment matching based, low order approximations for linear systems. Systems & Control Letters, 47-56 (2014) · Zbl 1283.93060 |
| [90] | Ionescu, T. C., & Iftime, O. V. (2012). Moment matching with prescribed poles and zeros for infinite-dimensional systems. (pp. 1412-1417). |
| [91] | Ionescu, T. C., Iftime, O. V., & S̨tefan, R. (2023). A moment matching-based loop shaping design with closed-loop pole placement. In Proceedings of the 21st European control conference |
| [92] | Isidori, A. |
| [93] | Jaimoukha, I. M.; Kasenally, E. M., Implicitly restarted Krylov subspace methods for stable partial realizations. SIAM Journal on Matrix Analysis and Applications, 3, 633-652 (1997) · Zbl 0873.65065 |
| [94] | Kalman, R. E.; Falb, P. L.; Arbib, M. A. |
| [95] | Kavranoğlu, D.; Bettayeb, M., Characterization of the solution to the optimal \(H_\infty\) model reduction problem. Systems & Control Letters, 2, 99-107 (1993) · Zbl 0782.93021 |
| [96] | Kimura, H., A canonical form for partial realization of covariance sequences (1983), University of Osaka: University of Osaka Japan |
| [97] | Kimura, H., Positive partial realization of covariance sequences. Modeling, Identification and Robust Control, 499-513 (1986) · Zbl 0604.62094 |
| [98] | Krener, A. J.; Xiao, M., Nonlinear observer design in the Siegel domain. SIAM Journal on Control and Optimization, 3, 932-953 (2002) · Zbl 1052.93013 |
| [99] | Kunisch, K.; Volkwein, S., Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition. Journal of Optimization Theory and Applications, 2, 345-371 (1999) · Zbl 0949.93039 |
| [100] | Kunisch, K.; Volkwein, S., Proper orthogonal decomposition for optimality systems. ESAIM. Mathematical Modelling and Numerical Analysis, 01, 1-23 (2008) · Zbl 1141.65050 |
| [101] | Lall, S.; Beck, C., Error bounds for balanced model reduction of linear time-varying systems. IEEE Transactions on Automatic Control, 6, 946-956 (2003) · Zbl 1364.93115 |
| [102] | Lall, S.; Krysl, P.; Marsden, J., Structure-preserving model reduction for mechanical systems. Physica D, 304-318 (2003) · Zbl 1041.70011 |
| [103] | Lall, S.; Marsden, J. E.; Glavaski, S., A subspace approach to balanced truncation for model reduction of nonlinear control systems. International Journal on Robust and Nonlinear Control, 519-535 (2002) · Zbl 1006.93010 |
| [104] | Laub, A.; Heath, M.; Paige, C.; Ward, R., Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms. IEEE Transactions on Automatic Control, 2, 115-122 (1987) · Zbl 0624.93025 |
| [105] | Li, R. C.; Bai, Z., Structure-preserving model reduction using a Krylov subspace projection formulation. Communications in Mathematical Sciences, 2, 179-199 (2005) · Zbl 1100.65028 |
| [106] | Li, J. R.; White, J., Reduction of large circuit models via low rank approximate gramians. International Journal of Applied Mathematics and Computer Science, 1151-1171 (2001) · Zbl 0995.93027 |
| [107] | Liu, Y.; Anderson, B. D.O., Controller reduction via stable factorization and balancing. International Journal of Control, 2, 507-531 (1986) · Zbl 0604.93020 |
| [108] | Mäkilä, P. M.; Partington, J. R., Shift operator induced approximations of delay systems. SIAM Journal on Control and Optimization, 6, 1897-1912 (1999) · Zbl 0935.93047 |
| [109] | Mao, J., & Scarciotti, G. (2022a). Data-Driven Model Reduction by Moment Matching for Linear Systems through a Swapped Interconnection. In Proceedings of the 20th European control conference |
| [110] | Mao, J.; Scarciotti, G., Data-driven model reduction by two-sided moment matching (2022), arXiv:2212.08589 |
| [111] | Mao, J., & Scarciotti, G. (2024). Model Reduction by Moment Matching under Explicit Filters: A Swapped Interconnection Perspective. In Proceedings of the 22th European control conference |
| [112] | Mayo, A. J.; Antoulas, A. C., A framework for the solution of the generalized realization problem. Linear Algebra and its Applications, 2-3, 634-662 (2007) · Zbl 1118.93029 |
| [113] | Mellone, A.; Scarciotti, G., Output regulation of linear stochastic systems. IEEE Transactions on Automatic Control, 4, 1728-1743 (2022) · Zbl 1537.93249 |
| [114] | Meyer, D. G., Fractional balanced reduction: model reduction via a fractional representation. IEEE Transactions on Automatic Control, 12, 1341-1345 (1990) · Zbl 0723.93011 |
| [115] | Moore, B. C., Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Transactions on Automatic Control, 1, 17-32 (1981) · Zbl 0464.93022 |
| [116] | Moreschini, A., Simard, J. D., & Astolfi, A. (2023a). Model Reduction for Linear Port-Hamiltonian Systems in the Loewner Framework. In 22nd IFAC world congress |
| [117] | Moreschini, A., Simard, J. D., & Astolfi, A. (2023b). Model Reduction in the Loewner Framework for Second-Order Network Systems On Graphs. In Proceedings of the 62nd IEEE conference on decision and control |
| [118] | Mullis, C.; Roberts, R., Synthesis of minimum roundoff noise fixed point digital filters. IEEE Transactions on Circuits and Systems, 9, 551-562 (1976) · Zbl 0342.93066 |
| [119] | Munk, C., Fixed income modelling (2011), OUP Oxford |
| [120] | Niu, Z., Zhang, H., & Scarciotti, G. (2024). Full-Information Output Regulation of Linear Systems with Non-periodic Non-smooth Exogenous Signals. In Proceedings of the 22th European control conference |
| [121] | Odabasioglu, A.; Celik, M.; Pileggi, L. T., PRIMA: passive reduced-order interconnect macromodeling algorithm. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 8, 645-654 (1998) |
| [122] | Øksendal, B. |
| [123] | Padoan, A., Model reduction by least squares moment matching for linear and nonlinear systems. IEEE Transactions on Automatic Control, 1-8 (2023), (in press) |
| [124] | Padoan, A., & Astolfi, A. (2014). Model reduction by moment matching for ZIP systems. In Proceedings of the 53rd IEEE conference on decision and control |
| [125] | Padoan, A., & Astolfi, A. (2017a). Model reduction by moment matching at isolated singularities for linear systems: a complex analytic approach. In IFAC-PapersOnLine - 20th IFAC world congress, vol. 50, no. 1 |
| [126] | Padoan, A., & Astolfi, A. (2017b). Model reduction by moment matching at isolated singularities for linear systems: A geometric approach. In Proceedings of the 56th IEEE conference on decision and control |
| [127] | Padoan, A.; Astolfi, A., Singularities and moments of nonlinear systems. IEEE Transactions on Automatic Control, 8, 3647-3654 (2020) · Zbl 1533.93257 |
| [128] | Padoan, A., Scarciotti, G., & Astolfi, A. (2016a). A geometric characterisation of persistently exciting signals generated by continuous-time autonomous systems. In IFAC symposium on nonlinear control systems |
| [129] | Padoan, A., Scarciotti, G., & Astolfi, A. (2016b). A geometric characterisation of the persistence of excitation condition for sequences generated by discrete-time autonomous systems. In Proceedings of the 55th IEEE conference on decision and control |
| [130] | Padoan, A.; Scarciotti, G.; Astolfi, A., A geometric characterization of the persistence of excitation condition for the solutions of autonomous systems. IEEE Transactions on Automatic Control, 11, 5666-5677 (2017) · Zbl 1390.93224 |
| [131] | Penzl, T., Algorithms for model reduction of large dynamical systems. Linear Algebra and its Applications - Special Issue on Order Reduction of Large-Scale Systems, 2-3, 322-343 (2006) · Zbl 1092.65053 |
| [132] | Pernebo, L.; Silverman, L., Model reduction via balanced state space representations. IEEE Transactions on Automatic Control, 2, 382-387 (1982) · Zbl 0482.93024 |
| [133] | Phillips, J. R. (2000). Projection frameworks for model reduction of weakly nonlinear systems. In Proceedings of the 37th design automation conference |
| [134] | Phillips, J. R., Projection-based approaches for model reduction of weakly nonlinear, time-varying systems. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2, 171-187 (2003) |
| [135] | Phillips, J.; Daniel, L.; Silveira, L. M., Guaranteed passive balancing transformations for model order reduction. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 8, 1027-1041 (2003) |
| [136] | Phillips, J. R.; Silveira, L. M., Poor man’s TBR: a simple model reduction scheme. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 1, 43-55 (2005) |
| [137] | Pillage, L. T.; Rohrer, R. A., Asymptotic waveform evaluation for timing analysis. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 4, 352-366 (1990) |
| [138] | Polyuga, R. V.; Van der Schaft, A., Structure preserving model reduction of port-Hamiltonian systems by moment matching at infinity. Automatica, 4, 665-672 (2010) · Zbl 1193.93085 |
| [139] | Polyuga, R. V.; Van der Schaft, A., Structure preserving moment matching for port-Hamiltonian systems: Arnoldi and lanczos. IEEE Transactions on Automatic Control, 6, 1458-1462 (2011) · Zbl 1368.93076 |
| [140] | Polyuga, R. V.; Van der Schaft, A., Effort- and flow-constraint reduction methods for structure preserving model reduction of port-Hamiltonian systems. Systems & Control Letters, 3, 412-421 (2012) · Zbl 1250.93019 |
| [141] | Rabiei, P., & Pedram, M. (1999). Model order reduction of large circuits using balanced truncation. In Proceedings of the Asia and South Pacific design automation conference |
| [142] | Reis, T.; Stykel, T., Positive real and bounded real balancing for model reduction of descriptor systems. International Journal of Control, 1, 74-88 (2010) · Zbl 1184.93026 |
| [143] | Rewienski, M.; White, J., A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2, 155-170 (2003) |
| [144] | Safonov, M. G.; Chiang, R. Y., A Schur method for balanced-truncation model reduction. IEEE Transactions on Automatic Control, 7, 729-733 (1989) · Zbl 0687.93027 |
| [145] | Safonov, M. G.; Chiang, R. Y.; Limebeer, D. J.N., Optimal Hankel model reduction for nonminimal systems. IEEE Transactions on Automatic Control, 4, 496-502 (1990) · Zbl 0704.93012 |
| [146] | Sandberg, H., A case study in model reduction of linear time-varying systems. Automatica, 3, 467-472 (2006) · Zbl 1121.93331 |
| [147] | Sandberg, H.; Rantzer, A., Balanced truncation of linear time-varying systems. IEEE Transactions on Automatic Control, 2, 217-229 (2004) · Zbl 1365.93062 |
| [148] | Saraswat, D., Achar, R., & Nakhla, M. (2005). Projection based fast passive compact macromodeling of high-speed VLSI circuits and interconnects. In 18th international conference on VLSI design held jointly with 4th international conference on embedded systems design |
| [149] | Scarciotti, G. (2015a). Model reduction by moment matching for linear singular systems. In Proceedings of the 54th IEEE conference on decision and control |
| [150] | Scarciotti, G. (2015b). Model Reduction of Power Systems with Preservation of Slow and Poorly Damped Modes. In IEEE power & energy society general meeting |
| [151] | Scarciotti, G., Approximation, analysis and control of large-scale systems (2016), Imperial College London, (Ph.D. thesis) |
| [152] | Scarciotti, G. (2016b). Moment matching for nonlinear differential-algebraic equations. In Proceedings of the 55th IEEE conference on decision and control |
| [153] | Scarciotti, G. (2017a). Discontinuous phasor model of an inductive power transfer system. In 2017 IEEE wireless power transfer conference |
| [154] | Scarciotti, G., Low computational complexity model reduction of power systems with preservation of physical characteristics. IEEE Transactions on Power Systems, 1, 743-752 (2017) |
| [155] | Scarciotti, G., Steady-state matching and model reduction for systems of differential-algebraic equations. IEEE Transactions on Automatic Control, 10, 5372-5379 (2017) · Zbl 1390.93191 |
| [156] | Scarciotti, G., & Astolfi, A. (2014a). Model reduction by moment matching for linear time-delay systems. In IFAC proceedings volumes - 19th IFAC world congress, vol. 47, no. 3 |
| [157] | Scarciotti, G., & Astolfi, A. (2014b). Model reduction by moment matching for nonlinear time-delay systems. In Proceedings of the 53rd IEEE conference on decision and control |
| [158] | Scarciotti, G., & Astolfi, A. (2015a). Characterization of the moments of a linear system driven by explicit signal generators. In Proceedings of the 2015 American control conference |
| [159] | Scarciotti, G., & Astolfi, A. (2015b). Model Reduction for linear systems and linear time-delay systems from input/output data. In Proceedings of the 14th European control conference |
| [160] | Scarciotti, G., & Astolfi, A. (2015c). Model Reduction for nonlinear systems and nonlinear time-delay systems from input/output data. In Proceedings of the 54th IEEE conference on decision and control |
| [161] | Scarciotti, G.; Astolfi, A., Model reduction by matching the steady-state response of explicit signal generators. IEEE Transactions on Automatic Control, 7, 1995-2000 (2016) · Zbl 1359.93081 |
| [162] | Scarciotti, G., & Astolfi, A. (2016b). Model reduction for hybrid systems with state-dependent jumps. In IFAC symposium nonlinear control systems |
| [163] | Scarciotti, G.; Astolfi, A., Model reduction of neutral linear and nonlinear time-invariant time-delay systems with discrete and distributed delays. IEEE Transactions on Automatic Control, 6, 1438-1451 (2016) · Zbl 1359.93082 |
| [164] | Scarciotti, G.; Astolfi, A., Moment-based discontinuous phasor transform and its application to the steady-state analysis of inverters and wireless power transfer systems. IEEE Transactions on Power Electronics, 12, 8448-8460 (2016) |
| [165] | Scarciotti, G., & Astolfi, A. (2016e). Moments at “discontinuous signals” with applications: model reduction for hybrid systems and phasor transform for switching circuits. In Proceedings of the 22nd international symposium on mathematical theory of networks and systems |
| [166] | Scarciotti, G., & Astolfi, A. (2016f). A note on the electrical equivalent of the moment theory. In Proceedings of the 2016 American control conference |
| [167] | Scarciotti, G.; Astolfi, A., Data-driven model reduction by moment matching for linear and nonlinear systems. Automatica, 340-351 (2017) · Zbl 1371.93045 |
| [168] | Scarciotti, G.; Astolfi, A., Nonlinear model reduction by moment matching. Foundations and Trends® in Systems and Control, 3-4, 224-409 (2017) |
| [169] | Scarciotti, G.; Astolfi, A., A review on model reduction by moment matching for nonlinear systems, 29-52 · Zbl 1414.93048 |
| [170] | Scarciotti, G., Jiang, Z. P., & Astolfi, A. (2016). Constrained optimal reduced-order models from input/output data. In Proceedings of the 55th IEEE conference on decision and control |
| [171] | Scarciotti, G.; Jiang, Z. P.; Astolfi, A., Data-driven constrained optimal model reduction. European Journal of Control (2019) |
| [172] | Scarciotti, G., & Teel, A. R. (2017a). Model Order Reduction for Stochastic Nonlinear Systems. In Proceedings of the 56th IEEE conference on decision and control |
| [173] | Scarciotti, G., & Teel, A. R. (2017b). Model Order Reduction of Stochastic Linear Systems by Moment Matching. In 20th IFAC world congress |
| [174] | Scarciotti, G.; Teel, A. R., On moment matching for stochastic systems. IEEE Transactions on Automatic Control, 2, 541-556 (2021) · Zbl 1537.93113 |
| [175] | Scarciotti, G., Teel, A. R., & Astolfi, A. (2017). Model reduction for linear differential inclusions: moment-set and time-variance. In Proceedings of the 2017 American control conference |
| [176] | Scherpen, J. M.A., Balancing for nonlinear systems. Systems & Control Letters, 2, 143-153 (1993) · Zbl 0785.93042 |
| [177] | Scherpen, J. M.A.; Gray, W. S., Minimality and local state decompositions of a nonlinear state space realization using energy functions. IEEE Transactions on Automatic Control, 11, 2079-2086 (2000) · Zbl 0989.93017 |
| [178] | Scherpen, J. M.A.; Gray, W. S., Nonlinear Hilbert adjoints: Properties and applications to Hankel singular value analysis. Nonlinear Analysis. Theory, Methods & Applications, 5, 883-901 (2002) · Zbl 1025.47043 |
| [179] | Scherpen, J. M.A.; Van der Schaft, A. J., Normalized coprime factorizations and balancing for unstable nonlinear systems. International Journal of Control, 6, 1193-1222 (1994) · Zbl 0813.93018 |
| [180] | Schulze, P., Ionescu, T., & Scherpen, J. (2016). Families of moment matching-based reduced order models for linear descriptor systems. In Proceedings of the 15th European control conference |
| [181] | Shakib, M. F., Scarciotti, G., Jungers, M., Pogromsky, A. Y., Pavlov, A., & van de Wouw, N. (2021). Optimal \(\mathcal{H}_\infty\) Proceedings of the 60th IEEE conference on decision and control |
| [182] | Shakib, M., Scarciotti, G., Pogromsky, A., Pavlov, A., & van de Wouw, N. (2021). Model Reduction by Moment Matching for Convergent Lur’e-Type Models. In Proceedings of the 2021 American control conference |
| [183] | Shakib, M.; Scarciotti, G.; Pogromsky, A.; Pavlov, A.; van de Wouw, N., Model reduction by moment matching with preservation of global stability for a class of nonlinear models. Automatica (2023) · Zbl 1522.93047 |
| [184] | Shakib, M.; Scarciotti, G.; Pogromsky, A.; Pavlov, A.; van de Wouw, N., Time-domain moment matching for multiple-input multiple-output linear time-invariant models. Automatica (2023) · Zbl 1519.93044 |
| [185] | Simard, J. D., Interpolation and model reduction of nonlinear systems in the Loewner framework (2023), Imperial College London, (Ph.D. thesis) |
| [186] | Simard, J. D., & Astolfi, A. (2019). An interconnection-based interpretation of the Loewner matrices. In Proceedings of the 58th IEEE conference on decision and control |
| [187] | Simard, J. D., & Astolfi, A. (2020a). Loewner functions for linear time-varying systems with applications to model reduction. In IFAC-PapersOnLine, vol. 53, no. 2 |
| [188] | Simard, J. D., & Astolfi, A. (2020b). Online Estimation of the Loewner Matrices. In Proceedings of the 59th IEEE conference on decision and control |
| [189] | Simard, J. D., & Astolfi, A. (2021a). Loewner Functions and Model Order Reduction for Nonlinear Input-Affine Descriptor Systems. In Proceedings of the 60th IEEE conference on decision and control |
| [190] | Simard, J. D.; Astolfi, A., Nonlinear model reduction in the Loewner framework. IEEE Transactions on Automatic Control, 12, 5711-5726 (2021) · Zbl 1536.93115 |
| [191] | Simard, J. D., & Astolfi, A. (2022a). Loewner Functions for a Class of Nonlinear Differential-Algebraic Systems. In Proceedings of the 61st IEEE conference on decision and control |
| [192] | Simard, J. D., & Astolfi, A. (2022b). Regularization of Underconstrained Interpolants in the Loewner Framework. In Proceedings of the 20th European control conference |
| [193] | Simard, J. D.; Astolfi, A., On the construction and parameterization of interpolants in the Loewner framework. Automatica (2023) |
| [194] | Simard, J. D., Cheng, X., & Moreschini, A. (2023). Interpolants With Second-Order Structure in the Loewner Framework. In 22nd IFAC world congress |
| [195] | Simard, J. D., Moreschini, A., & Astolfi, A. (2023a). Moment Matching for Nonlinear Systems of Second-Order Equations. In Proceedings of the 62nd IEEE conference on decision and control |
| [196] | Simard, J. D., Moreschini, A., & Astolfi, A. (2023b). Parameterization of All Moment Matching Interpolants. In Proceedings of the 21st European control conference |
| [197] | Soberg, J., Fujimoto, K., & Glad, T. (2007). Model reduction of nonlinear differential-algebraic equations. In IFAC symposium nonlinear control systems, vol. 7 |
| [198] | Sorensen, D.; Antoulas, A., The sylvester equation and approximate balanced reduction. Linear Algebra and its Applications, Fourth Special Issue on Linear Systems and Control, 671-700 (2002) · Zbl 1023.93012 |
| [199] | Tombs, M. S.; Postlethwaite, I., Truncated balanced realization of a stable non-minimal state-space system. International Journal of Control, 4, 1319-1330 (1987) · Zbl 0642.93015 |
| [200] | Van Dooren, P. M., Gramian based model reduction of large-scale dynamical systems. Chapman and Hall CRC Research Notes in Mathematics, 231-248 (2000) |
| [201] | Van Dooren, P.; Gallivan, K. A.; Absil, P. A., \( \mathcal{H}_2\)-Optimal model reduction of MIMO systems. Applied Mathematics Letters, 12, 1267-1273 (2008) · Zbl 1182.93034 |
| [202] | Varga, A., Minimal realization procedures based on balancing and related techniques, 733-761 |
| [203] | Verriest, E., & Gray, W. (1998). Dynamics near limit cycles: Model reduction and sensitivity. In Symposium on mathematical theory of networks and systems |
| [204] | Willcox, K.; Peraire, J., Balanced model reduction via the proper orthogonal decomposition. American Institute of Aeronautics and Astronautics, 11, 2323-2330 (2002) |
| [205] | Yan, B., Tan, S. X. D., Liu, P., & McGaughy, B. (2007). Passive Interconnect Macromodeling Via Balanced Truncation of Linear Systems in Descriptor Form. In 2007 Asia and South Pacific design automation conference |
| [206] | Yong, J.; Zhou, X. Y. |
| [207] | Yoon, M. G.; Lee, B. H., A new approximation method for time-delay systems. IEEE Transactions on Automatic Control, 7, 1008-1012 (1997) · Zbl 0889.93021 |
| [208] | Zadeh, L. A.; Desoer, C. A. |
| [209] | Zhao, Z., Mao, J., & Scarciotti, G. (2024). Strategies to Alleviate the Impact of Noise in Data-Driven Model Order Reduction by Moment Matching. In Proceedings of the 22th European control conference |
| [210] | Zhou, K.; Salomon, G.; Wu, E., Balanced realization and model reduction for unstable systems. International Journal of Robust and Nonlinear Control, 3, 183-198 (1999) · Zbl 0949.93018 |
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