On Dirac structure of infinite-dimensional stochastic port-Hamiltonian systems

Authors

François Lamoline, Anthony Hastir

Abstract

Stochastic infinite-dimensional port-Hamiltonian systems (SPHSs) with multiplicative Gaussian white noise are considered. In this article we extend the notion of Dirac structure for deterministic distributed parameter port-Hamiltonian systems to a stochastic ones by adding some additional stochastic ports. Using the Stratonovich formalism of the stochastic integral, the proposed extended interconnection of ports for SPHSs is proved to still form a Dirac structure. This constitutes our main contribution. We then deduce that the interconnection between (stochastic) Dirac structures is again a (stochastic) Dirac structure under some assumptions. These interconnection results are applied on a system composed of a stochastic vibrating string actuated at the boundary by a mass–spring system with external input and output. This work is motivated by the problem of boundary control of SPHSs and will serve as a foundation to the development of stabilizing methods.

Keywords

Infinite-dimensional systems; Stochastic partial differential equations; Dirac structures; Boundary control

Citation

• Journal: European Journal of Control
• Year: 2024
• Volume: 75
• Issue:
• Pages: 100924
• Publisher: Elsevier BV
• DOI: 10.1016/j.ejcon.2023.100924

BibTeX

@article{Lamoline_2024,
  title={{On Dirac structure of infinite-dimensional stochastic port-Hamiltonian systems}},
  volume={75},
  ISSN={0947-3580},
  DOI={10.1016/j.ejcon.2023.100924},
  journal={European Journal of Control},
  publisher={Elsevier BV},
  author={Lamoline, François and Hastir, Anthony},
  year={2024},
  pages={100924}
}

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