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Mathematics > Optimization and Control

arXiv:2210.06358 (math)
[Submitted on 12 Oct 2022]

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

Authors:François Lamoline, Anthony Hastir
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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.
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:2210.06358 [math.OC]
  (or arXiv:2210.06358v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2210.06358

Submission history

From: Anthony Hastir [view email]
[v1] Wed, 12 Oct 2022 16:10:25 UTC (93 KB)
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