Model Reduction for Fractional-Order Port-Hamiltonian Systems in the Loewner Framework
Authors
Zixi Guan, Rui Chen, Jinhua Zhang, Yiheng Wei
Abstract
No available
Citation
- Journal: 2025 4th Conference on Fully Actuated System Theory and Applications (FASTA)
- Year: 2025
- Volume:
- Issue:
- Pages: 348–353
- Publisher: IEEE
- DOI: 10.1109/fasta65681.2025.11138172
BibTeX
@inproceedings{Guan_2025,
title={{Model Reduction for Fractional-Order Port-Hamiltonian Systems in the Loewner Framework}},
DOI={10.1109/fasta65681.2025.11138172},
booktitle={{2025 4th Conference on Fully Actuated System Theory and Applications (FASTA)}},
publisher={IEEE},
author={Guan, Zixi and Chen, Rui and Zhang, Jinhua and Wei, Yiheng},
year={2025},
pages={348--353}
}
References
- Antoulas, A. C. Approximation of Large-Scale Dynamical Systems. (2005) doi:10.1137/1.9780898718713 – 10.1137/1.9780898718713
- Benner, P., Gugercin, S. & Willcox, K. A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems. SIAM Rev. 57, 483–531 (2015) – 10.1137/130932715
- Mainardi, F. Fractional Calculus and Waves in Linear Viscoelasticity. (2010) doi:10.1142/p614 – 10.1142/p614
- Hilfer, R. Applications of Fractional Calculus in Physics. (2000) doi:10.1142/3779 – 10.1142/3779
- Magin, R. L. Fractional Calculus in Bioengineering, Part 1. Crit Rev Biomed Eng 32, 1–104 (2004) – 10.1615/critrevbiomedeng.v32.10
- Brugnoli, A., Rashad, R., Zhang, Y. & Stramigioli, S. Finite element hybridization of port-Hamiltonian systems. Applied Mathematics and Computation 498, 129377 (2025) – 10.1016/j.amc.2025.129377
- Deng, Frequency-domain fitting for fractional-order system approximation. Automatica (2019)
- Maione, Fractional-order moment matching for reducedorder modeling. Communications in Nonlinear Science (2016)
- van der Schaft, A. J. & Maschke, B. M. Port-Hamiltonian Systems on Graphs. SIAM J. Control Optim. 51, 906–937 (2013) – 10.1137/110840091
- Cardoso-Ribeiro, Port-hamiltonian modeling of fluidstructure interaction. IEEE Transactions on Control Systems Technology (2019)
- van der Schaft, Network dynamics in port-hamiltonian form. Annual Reviews in Control (2017)
- Gugercin, S., Polyuga, R. V., Beattie, C. & van der Schaft, A. Structure-preserving tangential interpolation for model reduction of port-Hamiltonian systems. Automatica 48, 1963–1974 (2012) – 10.1016/j.automatica.2012.05.052
- Antoulas, Interpolatory model reduction via the loewner framework. SIAM Journal on Scientific Computing (2010)
- Mayo, A. J. & Antoulas, A. C. A framework for the solution of the generalized realization problem. Linear Algebra and its Applications 425, 634–662 (2007) – 10.1016/j.laa.2007.03.008
- Moreschini, A., Simard, J. D. & Astolfi, A. Data-driven model reduction for port-Hamiltonian and network systems in the Loewner framework. Automatica 169, 111836 (2024) – 10.1016/j.automatica.2024.111836
- 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 61, 412–421 (2012) – 10.1016/j.sysconle.2011.12.008
- Jardón-Kojakhmetov, H., Muñoz-Arias, M. & Scherpen, J. M. A. Model reduction of a flexible-joint robot: a port-Hamiltonian approach. IFAC-PapersOnLine 49, 832–837 (2016) – 10.1016/j.ifacol.2016.10.269
- Palitta, D. & Lefteriu, S. An Efficient, Memory-Saving Approach for the Loewner Framework. J Sci Comput 91, (2022) – 10.1007/s10915-022-01800-3
- Wei, Y., Cao, J., Chen, Y. & Wei, Y. The proof of Lyapunov asymptotic stability theorems for Caputo fractional order systems. Applied Mathematics Letters 129, 107961 (2022) – 10.1016/j.aml.2022.107961
- Casagrande, D., Krajewski, W. & Viaro, U. The Integer–Order Approximation of Fractional–Order Systems in The Loewner Framework. IFAC-PapersOnLine 52, 43–48 (2019) – 10.1016/j.ifacol.2019.06.008
- van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. FnT in Systems and Control 1, 173–378 (2014) – 10.1561/2600000002
- Abdalla, H. M. A., Casagrande, D., Krajewski, W. & Viaro, U. Loewner integer-order approximation of MIMO fractional-order systems. Applied Numerical Mathematics 198, 112–121 (2024) – 10.1016/j.apnum.2023.12.011
- Meng, L. et al. Minimal realization and approximation of commensurate linear fractional-order systems via Loewner matrix method. Mathematical Biosciences and Engineering 18, 1063–1076 (2021) – 10.3934/mbe.2021058
- Moreschini, A., Simard, J. D. & Astolfi, A. Model Reduction for Linear Port-Hamiltonian Systems in the Loewner Framework. IFAC-PapersOnLine 56, 9493–9498 (2023) – 10.1016/j.ifacol.2023.10.246
- Baziyad, M., Jarndal, A. & Bettayeb, M. A Model Order Reduction Technique Based on Balanced Truncation Method and Artificial Neural Networks. 2019 8th International Conference on Modeling Simulation and Applied Optimization (ICMSAO) 1–5 (2019) doi:10.1109/icmsao.2019.8880270 – 10.1109/icmsao.2019.8880270