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

François LAMOLINE, Anthony HASTIR

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Article number100924
JournalEuropean Journal of Control
Publication statusPublished - 30 Oct 2023


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


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