Energy Shaping of Distributed Port‐Hamiltonian Systems Based on Finite Volume Approximation

Authors

Fu Zheng, Ziwei Zhang, Sizhe Wang

Abstract

              This work introduces a semi‐discrete formulation for a class of infinite‐dimensional port‐Hamiltonian systems (PHS) through a finite volume approach. After spatial discretization, the resulting models maintain the core structural properties of PHS, including the underlying Dirac structure, which is preserved in the absence of external interconnections. A key aspect of this approach involves the integration of a finite‐dimensional controller with the infinite‐dimensional system through a power‐conserving interconnection. Furthermore, we establish a criterion for the existence of discrete analogs of Casimir functions in the discretized framework. The methodology is illustrated through its application to the Timoshenko beam model, where a discrete Casimir function is effectively constructed, reflecting the essential features of the continuous case.

Citation

• Journal: Mathematical Methods in the Applied Sciences
• Year: 2026
• Volume:
• Issue:
• Pages:
• Publisher: Wiley
• DOI: 10.1002/mma.70835

BibTeX

@article{Zheng_2026,
  title={{Energy Shaping of Distributed Port‐Hamiltonian Systems Based on Finite Volume Approximation}},
  ISSN={1099-1476},
  DOI={10.1002/mma.70835},
  journal={Mathematical Methods in the Applied Sciences},
  publisher={Wiley},
  author={Zheng, Fu and Zhang, Ziwei and Wang, Sizhe},
  year={2026}
}

Download the bib file

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