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

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, includin...

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Bibliographic Details
Published inEuropean journal of control Vol. 62; pp. 41 - 46
Main Author Lamoline, Francois
Format Journal Article
LanguageEnglish
Published Philadelphia Elsevier Ltd 01.11.2021
Elsevier Limited
Subjects
Boundary conditions
Boundary control
Boundary observation
Damping
Hamiltonian functions
Hilbert space
Infinite-dimensional systems
Integrals
Noise
Partial differential equations
Passivity
Port-Hamiltonian systems
Random variables
Stochastic partial differential equations
Stochastic systems
Boundary control
Stochastic partial differential equations
Infinite-dimensional systems
Boundary observation
Passivity
Port-Hamiltonian systems
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Summary: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.
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ISSN:0947-3580
1435-5671
DOI:10.1016/j.ejcon.2021.06.010