Energy-Preserving and Passivity-Consistent Numerical Discretization of Port-Hamiltonian Systems

In this paper we design discrete port-Hamiltonian systems systematically in two different ways, by applying discrete gradient methods and splitting methods respectively. The discrete port-Hamiltonian systems we get satisfy a discrete notion of passivity, which lets us, by choosing the input appropri...

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Bibliographic Details
Published inarXiv.org
Main Authors Celledoni, Elena, Eirik Hoel Høiseth
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 26.06.2017
Subjects
Asymptotic methods
Chaos theory
Hamiltonian functions
Integrators
Passivity
Test procedures
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Summary:In this paper we design discrete port-Hamiltonian systems systematically in two different ways, by applying discrete gradient methods and splitting methods respectively. The discrete port-Hamiltonian systems we get satisfy a discrete notion of passivity, which lets us, by choosing the input appropriately, make them globally asymptotically stable with respect to an equilibrium point. We test methods designed using the discrete gradient approach in numerical experiments, and the results are encouraging when compared to relevant existing integrators of identical order.
ISSN:2331-8422