Explicit Simplicial Discretization of Distributed-Parameter Port-Hamiltonian Systems
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.
Cite
@article{arxiv.1208.3549,
title = {Explicit Simplicial Discretization of Distributed-Parameter Port-Hamiltonian Systems},
author = {Marko Seslija and Jacquelien M. A. Scherpen and Arjan van der Schaft},
journal= {arXiv preprint arXiv:1208.3549},
year = {2013}
}