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Interpolation Conditions for Instant Data Consistency with Port-Hamiltonian Structure

  • Martina Vanelli
  • Nima Monshizadeh
  • Julien M. Hendrickx
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Abstract

We develop a data-driven framework for nonlinear port-Hamiltonian (pH) systems based on interpolation conditions to characterize consistency between observed data and structured dynamical models. Specifically, we derive necessary and sufficient conditions for the existence of a pH system with a smooth (convex) Hamiltonian instantly consistent with a given dataset, without requiring explicit parametrization. We further provide a semidefinite programming formulation to verify consistency with non-degenerate interconnection and dissipation structures. Our results provide a principled approach to assess instant data consistency with physical structure and pave the way for control design directly from data.

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Cite

BibTeXRIS
BibTeX
@misc{vanelli2026interpolation,
  title = {{Interpolation Conditions for Instant Data Consistency with Port-Hamiltonian Structure}},
  author = {Martina Vanelli and Nima Monshizadeh and Julien M. Hendrickx},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.31092},
  eprint = {2608.31092},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.31092},
}
RIS
TY  - UNPB
TI  - Interpolation Conditions for Instant Data Consistency with Port-Hamiltonian Structure
AU  - Martina Vanelli
AU  - Nima Monshizadeh
AU  - Julien M. Hendrickx
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.31092
UR  - https://arxiv.org/abs/2608.31092
AB  - We develop a data-driven framework for nonlinear port-Hamiltonian (pH) systems based on interpolation conditions to characterize consistency between observed data and structured dynamical models. Specifically, we derive necessary and sufficient conditions for the existence of a pH system with a smooth (convex) Hamiltonian instantly consistent with a given dataset, without requiring explicit parametrization. We further provide a semidefinite programming formulation to verify consistency with non-degenerate interconnection and dissipation structures. Our results provide a principled approach to assess instant data consistency with physical structure and pave the way for control design directly from data.
ER  -