Port-Hamiltonian Dynamic Mode Decomposition
Authors
Riccardo Morandin, Jonas Nicodemus, Benjamin Unger
Citation
- Journal: SIAM Journal on Scientific Computing
- Year: 2023
- Volume: 45
- Issue: 4
- Pages: A1690–A1710
- Publisher: Society for Industrial & Applied Mathematics (SIAM)
- DOI: 10.1137/22m149329x
BibTeX
@article{Morandin_2023,
title={{Port-Hamiltonian Dynamic Mode Decomposition}},
volume={45},
ISSN={1095-7197},
DOI={10.1137/22m149329x},
number={4},
journal={SIAM Journal on Scientific Computing},
publisher={Society for Industrial & Applied Mathematics (SIAM)},
author={Morandin, Riccardo and Nicodemus, Jonas and Unger, Benjamin},
year={2023},
pages={A1690--A1710}
}
References
- Altmann, R., Mehrmann, V. & Unger, B. Port-Hamiltonian formulations of poroelastic network models. Mathematical and Computer Modelling of Dynamical Systems vol. 27 429–452 (2021) – 10.1080/13873954.2021.1975137
- Annoni, J., Gebraad, P. & Seiler, P. Wind farm flow modeling using an input-output reduced-order model. 2016 American Control Conference (ACC) 506–512 (2016) doi:10.1109/acc.2016.7524964 – 10.1109/acc.2016.7524964
- Antoulas, A. C., Lefteriu, S. & Ionita, A. C. Chapter 8: A Tutorial Introduction to the Loewner Framework for Model Reduction. Model Reduction and Approximation 335–376 (2017) doi:10.1137/1.9781611974829.ch8 – 10.1137/1.9781611974829.ch8
- Beattie, C. A., Mehrmann, V. & Van Dooren, P. Robust port-Hamiltonian representations of passive systems. Automatica vol. 100 182–186 (2019) – 10.1016/j.automatica.2018.11.013
- Beattie, C., Mehrmann, V., Xu, H. & Zwart, H. Linear port-Hamiltonian descriptor systems. Mathematics of Control, Signals, and Systems vol. 30 (2018) – 10.1007/s00498-018-0223-3
- Benner, P., Goyal, P., Heiland, J. & Duff, I. P. Operator inference and physics-informed learning of low-dimensional models for incompressible flows. ETNA - Electronic Transactions on Numerical Analysis vol. 56 28–51 (2021) – 10.1553/etna_vol56s28
- Benner, P., Goyal, P. & Van Dooren, P. Identification of port-Hamiltonian systems from frequency response data. Systems & Control Letters vol. 143 104741 (2020) – 10.1016/j.sysconle.2020.104741
- Benner, P., Himpe, C. & Mitchell, T. On reduced input-output dynamic mode decomposition. Advances in Computational Mathematics vol. 44 1751–1768 (2018) – 10.1007/s10444-018-9592-x
- Borja P., IEEE Trans. Automat. Control (2021)
- Breiten, T., Morandin, R. & Schulze, P. Error bounds for port-Hamiltonian model and controller reduction based on system balancing. Computers & Mathematics with Applications vol. 116 100–115 (2022) – 10.1016/j.camwa.2021.07.022
- Breiten, T. & Unger, B. Passivity preserving model reduction via spectral factorization. Automatica vol. 142 110368 (2022) – 10.1016/j.automatica.2022.110368
- Deng, Y.-B., Hu, X.-Y. & Zhang, L. Least Squares Solution of BXAT=T over Symmetric, Skew-Symmetric, and Positive Semidefinite X. SIAM Journal on Matrix Analysis and Applications vol. 25 486–494 (2003) – 10.1137/s0895479802402491
- Gillis, N. & Sharma, P. On computing the distance to stability for matrices using linear dissipative Hamiltonian systems. Automatica vol. 85 113–121 (2017) – 10.1016/j.automatica.2017.07.047
- Gillis, N. & Sharma, P. A semi-analytical approach for the positive semidefinite Procrustes problem. Linear Algebra and its Applications vol. 540 112–137 (2018) – 10.1016/j.laa.2017.11.023
- Gugercin, S., Polyuga, R. V., Beattie, C. & van der Schaft, A. Structure-preserving tangential interpolation for model reduction of port-Hamiltonian systems. Automatica vol. 48 1963–1974 (2012) – 10.1016/j.automatica.2012.05.052
- Gustavsen, B. & Semlyen, A. Rational approximation of frequency domain responses by vector fitting. IEEE Transactions on Power Delivery vol. 14 1052–1061 (1999) – 10.1109/61.772353
- Heiland, J. & Unger, B. Identification of Linear Time-Invariant Systems with Dynamic Mode Decomposition. Mathematics vol. 10 418 (2022) – 10.3390/math10030418
- Higham N. J., Matrix Nearness Problems and Applications (1988)
- Jacob, B. & Zwart, H. J. Linear Port-Hamiltonian Systems on Infinite-Dimensional Spaces. (Springer Basel, 2012). doi:10.1007/978-3-0348-0399-1 – 10.1007/978-3-0348-0399-1
- Juang, J.-N. & Pappa, R. S. An eigensystem realization algorithm for modal parameter identification and model reduction. Journal of Guidance, Control, and Dynamics vol. 8 620–627 (1985) – 10.2514/3.20031
- Karniadakis, G. E. et al. Physics-informed machine learning. Nature Reviews Physics vol. 3 422–440 (2021) – 10.1038/s42254-021-00314-5
- Kotyczka, P. & Lefèvre, L. Discrete-time port-Hamiltonian systems based on Gauss-Legendre collocation. IFAC-PapersOnLine vol. 51 125–130 (2018) – 10.1016/j.ifacol.2018.06.035
- Kutz, J. N., Brunton, S. L., Brunton, B. W. & Proctor, J. L. Dynamic Mode Decomposition. (2016) doi:10.1137/1.9781611974508 – 10.1137/1.9781611974508
- Mayo, A. J. & Antoulas, A. C. A framework for the solution of the generalized realization problem. Linear Algebra and its Applications vol. 425 634–662 (2007) – 10.1016/j.laa.2007.03.008
- Nesterov Y., Introductory Lectures on Convex Optimization: A Basic Course (2003)
- Peherstorfer, B., Gugercin, S. & Willcox, K. Data-Driven Reduced Model Construction with Time-Domain Loewner Models. SIAM Journal on Scientific Computing vol. 39 A2152–A2178 (2017) – 10.1137/16m1094750
- Peherstorfer, B. & Willcox, K. Data-driven operator inference for nonintrusive projection-based model reduction. Computer Methods in Applied Mechanics and Engineering vol. 306 196–215 (2016) – 10.1016/j.cma.2016.03.025
- Polyuga, R. V. & van der Schaft, A. Structure Preserving Moment Matching for Port-Hamiltonian Systems: Arnoldi and Lanczos. IEEE Transactions on Automatic Control vol. 56 1458–1462 (2011) – 10.1109/tac.2011.2128650
- Polyuga, R. V. & van der Schaft, A. J. Effort- and flow-constraint reduction methods for structure preserving model reduction of port-Hamiltonian systems. Systems & Control Letters vol. 61 412–421 (2012) – 10.1016/j.sysconle.2011.12.008
- Proctor, J. L., Brunton, S. L. & Kutz, J. N. Dynamic Mode Decomposition with Control. SIAM Journal on Applied Dynamical Systems vol. 15 142–161 (2016) – 10.1137/15m1013857
- Raissi, M., Perdikaris, P. & Karniadakis, G. E. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics vol. 378 686–707 (2019) – 10.1016/j.jcp.2018.10.045
- Sato, K. & Sato, H. Structure-Preserving $H^2$ Optimal Model Reduction Based on the Riemannian Trust-Region Method. IEEE Transactions on Automatic Control vol. 63 505–512 (2018) – 10.1109/tac.2017.2723259
- SCHMID, P. J. Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics vol. 656 5–28 (2010) – 10.1017/s0022112010001217
- Schulze, P. & Unger, B. Data-driven interpolation of dynamical systems with delay. Systems & Control Letters vol. 97 125–131 (2016) – 10.1016/j.sysconle.2016.09.007
- Schulze, P., Unger, B., Beattie, C. & Gugercin, S. Data-driven structured realization. Linear Algebra and its Applications vol. 537 250–286 (2018) – 10.1016/j.laa.2017.09.030
- Schwerdtner, P. & Voigt, M. Adaptive Sampling for Structure-Preserving Model Order Reduction of Port-Hamiltonian Systems. IFAC-PapersOnLine vol. 54 143–148 (2021) – 10.1016/j.ifacol.2021.11.069
- Sharma, H., Wang, Z. & Kramer, B. Hamiltonian operator inference: Physics-preserving learning of reduced-order models for canonical Hamiltonian systems. Physica D: Nonlinear Phenomena vol. 431 133122 (2022) – 10.1016/j.physd.2021.133122
- H. Tu, J. et al. On dynamic mode decomposition: Theory and applications. Journal of Computational Dynamics vol. 1 391–421 (2014) – 10.3934/jcd.2014.1.391
- van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control vol. 1 173–378 (2014) – 10.1561/2600000002
- Werner, S. W. R., Gosea, I. V. & Gugercin, S. Structured vector fitting framework for mechanical systems. IFAC-PapersOnLine vol. 55 163–168 (2022) – 10.1016/j.ifacol.2022.09.089
- Wolf, T., Lohmann, B., Eid, R. & Kotyczka, P. Passivity and Structure Preserving Order Reduction of Linear Port-Hamiltonian Systems Using Krylov Subspaces. European Journal of Control vol. 16 401–406 (2010) – 10.3166/ejc.16.401-406