Solvability of Time-Varying Infinite-Dimensional Linear Port-Hamiltonian Systems

Authors

Mikael Kurula

Abstract

Thirty years after the introduction of port-Hamiltonian systems, interest in this system class still remains high among systems and control researchers. Very recently, Jacob and Laasri obtained strong results on the solvability and well-posedness of time-varying linear port-Hamiltonian systems with boundary control and boundary observation. In this article, we complement their results by discussing the solvability of linear, infinite-dimensional time-varying port-Hamiltonian systems not necessarily of boundary control type. The theory is illustrated on a system with a delay component in the state dynamics.

Citation

• Journal: IEEE Transactions on Automatic Control
• Year: 2024
• Volume: 69
• Issue: 7
• Pages: 4813–4819
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/tac.2024.3355852

BibTeX

@article{Kurula_2024,
  title={{Solvability of Time-Varying Infinite-Dimensional Linear Port-Hamiltonian Systems}},
  volume={69},
  ISSN={2334-3303},
  DOI={10.1109/tac.2024.3355852},
  number={7},
  journal={IEEE Transactions on Automatic Control},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Kurula, Mikael},
  year={2024},
  pages={4813--4819}
}

Download the bib file

References

• Maschke, B. M. & van der Schaft, A. J. Port-Controlled Hamiltonian Systems: Modelling Origins and Systemtheoretic Properties. IFAC Proceedings Volumes vol. 25 359–365 (1992) – 10.1016/s1474-6670(17)52308-3
• 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
• Golo, Interconnection structures in port-based modelling: Tools for analysis and simulation. (2002)
• Le Gorrec, Y., Zwart, H. & Maschke, B. Dirac structures and Boundary Control Systems associated with Skew-Symmetric Differential Operators. SIAM Journal on Control and Optimization vol. 44 1864–1892 (2005) – 10.1137/040611677
• Kurula, M., Zwart, H., van der Schaft, A. & Behrndt, J. Dirac structures and their composition on Hilbert spaces. Journal of Mathematical Analysis and Applications vol. 372 402–422 (2010) – 10.1016/j.jmaa.2010.07.004
• Kurula, Linear wave systems on $n$-D spatial domains. Int. J. Control (2015)
• Skrepek, N. Well-posedness of linear first order port-Hamiltonian Systems on multidimensional spatial domains. Evolution Equations & Control Theory vol. 10 965 (2021) – 10.3934/eect.2020098
• Augner, B. & Laasri, H. Exponential stability for infinite-dimensional non-autonomous port-Hamiltonian Systems. Systems & Control Letters vol. 144 104757 (2020) – 10.1016/j.sysconle.2020.104757
• Jacob, B. & Laasri, H. Well-posedness of infinite-dimensional non-autonomous passive boundary control systems. Evolution Equations & Control Theory vol. 10 385–409 (2021) – 10.3934/eect.2020072
• 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
• Malinen, J. & Staffans, O. J. Impedance Passive and Conservative Boundary Control Systems. Complex Analysis and Operator Theory vol. 1 279–300 (2007) – 10.1007/s11785-006-0009-3
• Gorbachuk, V. I. & Gorbachuk, M. L. Boundary Value Problems for Operator Differential Equations. (Springer Netherlands, 1991). doi:10.1007/978-94-011-3714-0 – 10.1007/978-94-011-3714-0
• Staffans, O. Well-Posed Linear Systems. (2005) doi:10.1017/cbo9780511543197 – 10.1017/cbo9780511543197
• Staffans, O. J. Passive and Conservative Continuous-Time Impedance and Scattering Systems. Part I: Well-Posed Systems. Mathematics of Control, Signals, and Systems (MCSS) vol. 15 291–315 (2002) – 10.1007/s004980200012
• Staffans, O. J. Passive and Conservative Infinite-Dimensional Impedance and Scattering Systems (From a Personal Point of View). The IMA Volumes in Mathematics and its Applications 375–413 (2003) doi:10.1007/978-0-387-21696-6_14 – 10.1007/978-0-387-21696-6_14
• Staffans, O. On scattering passive system nodes and maximal scattering dissipative operators. Proceedings of the American Mathematical Society vol. 141 1377–1383 (2012) – 10.1090/s0002-9939-2012-11887-8
• Kurula, M. Well-Posedness of Time-Varying Linear Systems. IEEE Transactions on Automatic Control vol. 65 4075–4089 (2020) – 10.1109/tac.2019.2954794
• Schnaubelt, R. & Weiss, G. Two classes of passive time-varying well-posed linear systems. Mathematics of Control, Signals, and Systems vol. 21 265–301 (2010) – 10.1007/s00498-010-0049-0