Passivity of boundary controlled and observed stochastic port-Hamiltonian systems subject to multiplicative and input noise

Authors

Francois Lamoline

Abstract

We study infinite-dimensional stochastic port-Hamiltonian systems (SPHSs) having multiplicative and boundary input noise. Using Itô and Stratonovich integrals on Hilbert spaces, a formal mathematical description of this specific class of stochastic systems is presented, and some properties, including almost sure and weak passivity, are investigated. By considering dissipative effects, we derive a condition for SPHSs to be weakly passive. Finally, the stochastic port-Hamiltonian framework and the passivity concepts are illustrated on the example of an inhomogeneous vibrating string subject to random damping and state noises.

Keywords

Boundary control; Boundary observation; Port-Hamiltonian systems; Stochastic partial differential equations; Infinite-dimensional systems; Passivity

Citation

• Journal: European Journal of Control
• Year: 2021
• Volume: 62
• Issue:
• Pages: 41–46
• Publisher: Elsevier BV
• DOI: 10.1016/j.ejcon.2021.06.010
• Note: 2021 European Control Conference Special Issue

BibTeX

@article{Lamoline_2021,
  title={{Passivity of boundary controlled and observed stochastic port-Hamiltonian systems subject to multiplicative and input noise}},
  volume={62},
  ISSN={0947-3580},
  DOI={10.1016/j.ejcon.2021.06.010},
  journal={European Journal of Control},
  publisher={Elsevier BV},
  author={Lamoline, Francois},
  year={2021},
  pages={41--46}
}

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