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PreprintCC BY 4.0arXiv

Nonlinear differential-algebraic systems with dissipative port-Hamiltonian structure

  • Volker Mehrmann
  • Arjan van der Schaft
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Abstract

Different representations of nonlinear dissipative Hamiltonian and port-Hamiltonian (pH) differential-algebraic equations (DAE) systems are derived and compared. Using global geometric and algebraic points of view, including singular Lagrange and Dirac structures, as well as Morse families and their skew counterparts, constraints are incorporated in the models. The results are illustrated specifically with constrained mechanical systems using kinematic and geometric constraints. The relation between the different representations is studied and in particular the conversion of Lagrange into Dirac algebraic constraints and vice versa is discussed. To incorporate dissipation also maximally monotone structures are studied.

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Cite

BibTeXRIS
BibTeX
@misc{mehrmann2026nonlinear,
  title = {{Nonlinear differential-algebraic systems with dissipative port-Hamiltonian structure}},
  author = {Volker Mehrmann and Arjan van der Schaft},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11455},
  eprint = {2610.11455},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11455},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Nonlinear differential-algebraic systems with dissipative port-Hamiltonian structure
AU  - Volker Mehrmann
AU  - Arjan van der Schaft
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11455
UR  - https://arxiv.org/abs/2610.11455
AB  - Different representations of nonlinear dissipative Hamiltonian and port-Hamiltonian (pH) differential-algebraic equations (DAE) systems are derived and compared. Using global geometric and algebraic points of view, including singular Lagrange and Dirac structures, as well as Morse families and their skew counterparts, constraints are incorporated in the models. The results are illustrated specifically with constrained mechanical systems using kinematic and geometric constraints. The relation between the different representations is studied and in particular the conversion of Lagrange into Dirac algebraic constraints and vice versa is discussed. To incorporate dissipation also maximally monotone structures are studied.
ER  -