Authors

A.J. van der Schaft, J. Wei

Abstract

We study a basic dynamical distribution network, modeled as a directed graph with storage variables corresponding to the vertices, and unknown but constant inflows and outflows. It is shown how standard PI-control, regulating the storage variables irrespective of the inflows and outflows, corresponds to associating with every edge of the graph a controller state variable, yielding a closed-loop port-Hamiltonian system. Furthermore, it will be shown how regulation is proved by modifying the total Hamiltonian of the port-Hamiltonian system into a Lyapunov function based on the vector of constant inflows and outflows. Subsequently, the results are extended to the case that the input variables are constrained, leading to non-smooth Lyapunov functions.

Keywords

consensus algorithms, directed graphs, non-smooth lyapunov function, pi controllers, port-hamiltonian systems, saturation

Citation

  • Journal: IFAC Proceedings Volumes
  • Year: 2012
  • Volume: 45
  • Issue: 19
  • Pages: 24–29
  • Publisher: Elsevier BV
  • DOI: 10.3182/20120829-3-it-4022.00033
  • Note: 4th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control

BibTeX

@article{van_der_Schaft_2012,
  title={{A Hamiltonian perspective on the control of dynamical distribution networks}},
  volume={45},
  ISSN={1474-6670},
  DOI={10.3182/20120829-3-it-4022.00033},
  number={19},
  journal={IFAC Proceedings Volumes},
  publisher={Elsevier BV},
  author={van der Schaft, A.J. and Wei, J.},
  year={2012},
  pages={24--29}
}

Download the bib file

References

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