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arXiv · 1208.3549

Explicit Simplicial Discretization of Distributed-Parameter Port-Hamiltonian Systems

Marko Seslija·Jacquelien M. A. Scherpen·Arjan van der Schaft
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Abstract

Simplicial Dirac structures as finite analogues of the canonical Stokes-Dirac structure, capturing the topological laws of the system, are defined on simplicial manifolds in terms of primal and dual cochains related by the coboundary operators. These finite-dimensional Dirac structures offer a framework for the formulation of standard input-output finite-dimensional port-Hamiltonian systems that emulate the behavior of distributed-parameter port-Hamiltonian systems. This paper elaborates on the matrix representations of simplicial Dirac structures and the resulting port-Hamiltonian systems on simplicial manifolds. Employing these representations, we consider the existence of structural invariants and demonstrate how they pertain to the energy shaping of port-Hamiltonian systems on simplicial manifolds.

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Marko Seslija, Jacquelien M. A. Scherpen, Arjan van der Schaft. 2012-08-17. Explicit Simplicial Discretization of Distributed-Parameter Port-Hamiltonian Systems. https://arxiv.org/abs/1208.3549

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