Discrete-time port-Hamiltonian systems based on Gauss-Legendre collocation

Authors

Paul Kotyczka, Laurent Lefèvre

Abstract

We introduce a family of discrete-time lossless input-state-output port-Hamiltonian systems based on numerical time integration with symplectic collocation schemes. For systems with non-zero input, symplecticity extends to the conservation of a discrete energy balance, based on which a discrete-time Dirac structure is defined. Using Gauss-Legendre collocation, the corresponding quadrature formula allows to quantify the discretization error for the supplied energy. On a linear example, backward error analysis and numerical experiments are performed in order to illustrate the accuracy of the resulting structure-preserving integration schemes.

Keywords

Port-Hamiltonian systems; Dirac structures; discrete-time systems; geometric numerical integration; symplectic methods

Citation

• Journal: IFAC-PapersOnLine
• Year: 2018
• Volume: 51
• Issue: 3
• Pages: 125–130
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2018.06.035
• Note: 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018

BibTeX

@article{Kotyczka_2018,
  title={{Discrete-time port-Hamiltonian systems based on Gauss-Legendre collocation}},
  volume={51},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2018.06.035},
  number={3},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Kotyczka, Paul and Lefèvre, Laurent},
  year={2018},
  pages={125--130}
}

Download the bib file

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