Matrix-valued Impedances with Fractional Derivatives and Integrals in Boundary Feedback Control: a port-Hamiltonian approach

Authors

Abstract

This paper discusses the passivity of the port-Hamiltonian formulation of a multivariable impedance matching boundary feedback of fractional order, expressed through diffusive representation. It is first shown in the 1D-wave equation case that the impedance matching boundary feedback can be written as a passive feedback on the boundary port variables. In the Euler-Bernoulli case, the impedance matching feedback matrix involves fractional derivatives and integrals. It is shown that the usual diffusive representation of such feedback is not formally a dissipative port-Hamiltonian system, even if from a frequency point of view this feedback proves passive.

Keywords

fractional differential equations; diffusive systems; pseudo-differential operators; hereditary mechanics; stability; numerical methods; boundary control of PDEs

Citation

Journal: IFAC-PapersOnLine
Year: 2015
Volume: 48
Issue: 13
Pages: 182–187
Publisher: Elsevier BV
DOI: 10.1016/j.ifacol.2015.10.236
Note: 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2015- Lyon, France, 4–7 July 2015

BibTeX

@article{Le_Gorrec_2015,
  title={{Matrix-valued Impedances with Fractional Derivatives and Integrals in Boundary Feedback Control: a port-Hamiltonian approach}},
  volume={48},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2015.10.236},
  number={13},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Le Gorrec, Yann and Matignon, Denis},
  year={2015},
  pages={182--187}
}

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References

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