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Model reduction techniques for linear constant coefficient port-Hamiltonian differential-algebraic systems

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Języki publikacji
EN
Abstrakty
EN
The aim of this paper is to combine model order reduction for differential-algebraic equations with port-Hamiltonian structure preservation. For this, we extend two classes of model reduction techniques (reduction of the Dirac structure and moment matching) to handle port-Hamiltonian differential-algebraic equations. The performance of the methods is investigated for benchmark examples, originating from semi-discretized flow problems and mechanical multibody systems.
Rocznik
Strony
125--152
Opis fizyczny
Bibliogr. 39 poz., rys.
Twórcy
  • Universit¨at Trier Lehrstuhl Modellierung und Numerik Universit¨atsring 15, D-54296 Trier, Germany
  • Universit¨at Trier Lehrstuhl Modellierung und Numerik Universit¨atsring 15, D-54296 Trier, Germany
  • Technische Universit¨at Berlin Institut fu¨r Mathematik, MA4-5 Straße des 17. Juni 136, D-10623 Berlin, Germany
Bibliografia
  • [1] Aliyev, N., Benner, P., Mengi, E., Schwerdtner, P. and Voigt, M. (2017) Large-scale computation of L∞-norms by a greedy subspace method. SIAM Journal on Matrix Analysis and Applications 38 (4), 1496–1516.
  • [2] Antoulas, A. C. (2005) Approximation of Large-Scale Dynamical Systems. SIAM Publications, Philadelphia.
  • [3] Beattie, C., Gugercin, S. and Mehrmann, V. (2017) Model reduction for large-scale dynamical systems with inhomogeneous initial conditions. Systems and Control Letters 99, 99–106.
  • [4] Beattie, C., Mehrmann, V., Xu, H. and Zwart, H. (2018) Linear portHamiltonian descriptor systems. Mathematics of Control, Signals, and Systems 30 (4), 1–27.
  • [5] Benner, P., Mehrmann, V. and Sorensen, D. C., eds. (2005) Dimension Reduction of Large-Scale Systems. Lecture Notes in Computational Science and Engineering, 45. Springer, Berlin.
  • [6] Benner, P. and Sokolov, V. I. (2006) Partial realization of descriptor systems. Systems and Control Letters 55 (11), 929–938.
  • [7] Benner, P. and Stykel, T. (2017) Model order reduction for differentialalgebraic equations: A survey. In: Surveys in Differential-Algebraic Equations. IV, 107–160. Springer, Heidelberg.
  • [8] Borggaard, J.T. and Gugercin, S. (2015) Model reduction for DAEs with an application to flow control. In: Active Flow and Combustion Control 2014, 381–396. Springer, Cham.
  • [9] Brenan, K. E., Campbell, S. L. and Petzold, L. R. (1996) Numerical Solution of Initial-Value Problems in Differential Algebraic Equations, 2nd edn. SIAM Publications, Philadelphia.
  • [10] Byers, R., Geerts, T. and Mehrmann, V. (1997) Descriptor systems without controllability at infinity. SIAM Journal on Control and Optimization 35 (2), 462–479.
  • [11] Campbell, S. L., Kunkel, P. and Mehrmann, V. (2012) Regularization of linear and nonlinear descriptor systems. In: Control and Optimization with Differential-Algebraic Constraints, Advances in Design and Control 23, 17– 36. SIAM Publications, Philadelphia.
  • [12] Chaturantabut, S., Beattie, C. and Gugercin, S. (2016) Structurepreserving model reduction for nonlinear port-Hamiltonian systems. SIAM Journal on Scientific Computing 38 (5), B837–B865.
  • [13] Egger, H., Kugler, T., Liljegren-Sailer, B., Marheineke, N. and Mehrmann, V. (2018) On structure-preserving model reduction for damped wave propagation in transport networks. SIAM Journal on Scientific Computing 40 (1), A331–A365.
  • [14] Emmrich, E. and Mehrmann, V. (2013) Operator differential-algebraic equations arising in fluid dynamics. Computer Methods in Applied Mathematics 13 (4), 443–470.
  • [15] Freund, R. W. (2005) Pad´e-type model reduction of second-order and higherorder linear dynamical systems. In: Dimension Reduction of Large-Scale Systems, 191–223. Springer, Berlin.
  • [16] Golub, G. H. and van Loan, C. F. (1996) Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD.
  • [17] Grabner, N., Mehrmann, V., Quraishi, S., Schr¨oder, C. and von Wag ner, U. (2016) Numerical methods for parametric model reduction in the simulation of disc brake squeal. Zeitschrift fu¨r Angewandte Mathematik und Mechanik 96 (12), 1388–1405.
  • [18] Gugercin, S., Polyuga, R. V., Beattie, C. and van der Schaft, A. (2012) Structure-preserving tangential interpolation for model reduction of port-Hamiltonian systems. Automatica 48 (9), 1963–1974.
  • [19] Gugercin, S., Polyuga, R. V., Beattie, C. and van der Schaft, A. (2009) Interpolation-based H2 model reduction for port-Hamiltonian systems. In: Proceedings of 48th IEEE Conference on Decision and Control, 5362– 5369. IEEE.
  • [20] Gugercin, S., Stykel, T. and Wyatt, S. (2013) Model reduction of descriptor systems by interpolatory projection methods. SIAM Journal on Scientific Computing 35 (5), B1010–B1033.
  • [21] Heinkenschloss, M., Sorensen, D. C. and Sun, K. (2008) Balanced truncation model reduction for a class of descriptor systems with application to the Oseen equations. SIAM Journal on Scientific Computing 30 (2), 1038–1063.
  • [22] Kotyczka, P. and Lef`evre, L. (2018) Discrete-time port-Hamiltonian systems: A definition based on symplectic integration. IFAC-Papers OnLine 51 (3), 125–130.
  • [23] Kunkel, P. and Mehrmann, V. (2006) Differential-Algebraic Equations. European Mathematical Society (EMS), Zurich.
  • [24] Mehl, C., Mehrmann, V. and Wojtylak, M. (2018) Linear algebra properties of dissipative port-Hamiltonian descriptor systems. SIAM Journal on Matrix Analysis and Applications 39 (3), 1489–1519.
  • [25] Mehrmann, V. and Stykel, T. (2005) Balanced truncation model reduction for large-scale systems in descriptor form. In: Dimension Reduction of LargeScale Systems, pp. 83–115. Springer, Berlin.
  • [26] Polyuga, R. V. and van der Schaft, A. (2011) Structure-preserving moment matching for port-Hamiltonian systems: Arnoldi and Lanczos. IEEE Transactions on Automatic Control 56 (6), 1458–1462.
  • [27] Polyuga, R. V. and van der Schaft, A. (2012) Effort- and flowconstraint reduction methods for structure-preserving model reduction of port-Hamiltonian systems. Systems and Control Letters 61 (3), 412–421.
  • [28] Polyuga, R. V. and van der Schaft, A. (2010) Structure-preserving model reduction of port-Hamiltonian systems by moment matching at infinity. Automatica 46 (4), 665–672.
  • [29] Riaza, R. (2008) Differential-Algebraic Systems. Analytical Aspects and Circuit Applications. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ.
  • [30] Saad, Y. (2003) Iterative Methods for Sparse Linear Systems, 2nd edn. SIAM Publications, Philadelphia.
  • [31] Saak, J., K¨ohler, M. and Benner, P. (2016) M-M.M.E.S.S. 1.0.1 – The matrix equations sparse solvers library. See also: www.mpimagdeburg.mpg.de/projects/mess.
  • [32] van der Schaft, A. (2013) Port-Hamiltonian differential-algebraic systems. In: Surveys in Differential-Algebraic Equations. I, 173–226. Springer, Heidelberg.
  • [33] van der Schaft, A. and Jeltsema, D. (2014) Port-Hamiltonian systems theory: An introductory overview. Foundations and Trends in Systems and Control 1 (2-3), 173–378.
  • [34] van der Schaft, A. and Maschke, B. (2018) Generalized port-Hamiltonian DAE systems. Systems and Control Letters 121, 31–37.
  • [35] Scholz, L. (2017) Condensed forms for linear port-Hamiltonian descriptor systems. Preprint 09–2017. Institut fu¨r Mathematik, TU Berlin.
  • [36] Stykel, T. (2006a) Balanced truncation model reduction for semidiscretized Stokes equation. Linear Algebra and its Applications 415 (2-3), 262–289.
  • [37] Stykel, T. (2006 b) On some norms for descriptor systems. IEEE Transactions on Automatic Control 51 (5), 842–847.
  • [38] Varga, A. (1991) Balancing free square-root algorithm for computing singular perturbation approximations. In: Proceedings of 30th IEEE Conference on Decision and Control, 2, 1062–1065. IEEE.
  • [39] Wolf, T., Lohmann, B., Eid, R. and Kotyczka, P. (2010) Passivity and structure preserving order reduction of linear port-Hamiltonian systems using Krylov subspaces. European Journal of Control 16 (4), 401–406.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9618fe73-8145-492f-a002-20fda29054e5
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