Brayton-Moser Formulation of High-Order Distributed Port-Hamiltonian Systems with One-Dimensional Spatial Domain

Authors

Alessandro Macchelli

Abstract

For a class of distributed port-Hamiltonian systems with dissipation characterised by high-order differential operators, one-dimensional domain, and boundary actuation and sensing, an equivalent Brayton-Moser formulation is obtained. The result is that the state evolution is described by a gradient equation with respect to a storage function, the “mixed-potential,” that has the dimensions of power. This is the main difference with respect to the port-Hamiltonian form, where the dynamic depends on the derivatives up to a certain order and with respect to the spatial coordinate of the gradient of the Hamiltonian function, i.e. of the total energy.

Citation

• Journal: IFAC-PapersOnLine
• Year: 2019
• Volume: 52
• Issue: 2
• Pages: 46–51
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2019.08.009
• Note: 3rd IFAC Workshop on Control of Systems Governed by Partial Differential Equations CPDE 2019- Oaxaca, Mexico, 20–24 May 2019

BibTeX

@article{Macchelli_2019,
  title={{Brayton-Moser Formulation of High-Order Distributed Port-Hamiltonian Systems with One-Dimensional Spatial Domain}},
  volume={52},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2019.08.009},
  number={2},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Macchelli, Alessandro},
  year={2019},
  pages={46--51}
}

Download the bib file

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