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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| Published in | European journal of control Vol. 62; pp. 41 - 46 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
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01.11.2021
Elsevier Limited |
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| 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. |
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| AbstractList | 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. |
| Author | Lamoline, Francois |
| Author_xml | – sequence: 1 givenname: Francois surname: Lamoline fullname: Lamoline, Francois email: francois.lamoline@uni.lu organization: University of Luxembourg, Luxembourg Centre for Systems Biomedicine, 6 avenue du Swing, Belvaux L-4367, Luxembourg |
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| Cites_doi | 10.1109/TAC.2017.2676619 10.1137/151002605 10.1109/TAC.2012.2229791 10.1109/TAC.2019.2954481 10.1109/TAC.2014.2315754 10.1137/040611677 10.1137/S0363012997317478 10.1080/17442509308833817 10.1016/0022-247X(81)90031-7 10.1137/S0363012992228726 10.1016/j.automatica.2018.07.031 10.1007/978-3-7643-8994-9 10.1017/CBO9781107295513 10.1016/S0393-0440(01)00083-3 10.1109/TAC.2016.2595263 |
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| Copyright | 2021 European Control Association 2021. European Control Association |
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| DOI | 10.1016/j.ejcon.2021.06.010 |
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| Keywords | Boundary control Stochastic partial differential equations Infinite-dimensional systems Boundary observation Passivity Port-Hamiltonian systems |
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| SubjectTerms | 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 |
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| Title | Passivity of boundary controlled and observed stochastic port-Hamiltonian systems subject to multiplicative and input noise |
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