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

2017/06/26 by Elena Celledoni, Celledoni, Elena, Eirik Hoel Høiseth +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #65P40 #ATP Synthase and ATPases Research #Control and Stability of Dynamical Systems #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1706.08621

openalex publication_date 2017/06/26 · openalex created_date 2017/07/14 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Energy stable Galerkin approximation of Hamiltonian and gradient systems
• Structure-Preserving Discretization and Model Reduction for Energy-Based Models

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