Authors

M. Schöberl, K. Schlacher

Abstract

In this paper we consider partial differential equations in a port-Hamiltonian setting. A crucial property of this system class, especially for control purposes, is the property to be able to link a power balance relation to the structure of the equations. However, to derive this power balance relation one has to take into account also the effects of energy flows via the boundary. This can be handled in a straightforward manner when the Hamiltonian depends on derivative variables of first order, e.g. by using integration by parts. If higher-order derivatives appear (higher-order field theory) then integration by parts cannot be used without due care, thus we suggest an approach by using the so-called Cartan-form. In this paper we concentrate on second-order theories in a port-Hamiltonian framework and we visualize the derivation of a power balance relation by using mechanical examples such as plates modeled as a first-order and as second-order field theory.

Keywords

Differential geometric methods; Hamiltonian Systems; Partial differential equations

Citation

  • Journal: IFAC-PapersOnLine
  • Year: 2015
  • Volume: 48
  • Issue: 13
  • Pages: 244–249
  • Publisher: Elsevier BV
  • DOI: 10.1016/j.ifacol.2015.10.247
  • Note: 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2015- Lyon, France, 4–7 July 2015

BibTeX

@article{Sch_berl_2015,
  title={{Port-Hamiltonian formulation for Higher-order PDEs}},
  volume={48},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2015.10.247},
  number={13},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Schöberl, M. and Schlacher, K.},
  year={2015},
  pages={244--249}
}

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References