Asymptotic Stabilisation of Distributed Port-Hamiltonian Systems by Boundary Energy-Shaping Control

Authors

Alessandro Macchelli, Yann Le Gorrec, Héctor Ramirez

Abstract

This paper illustrates a general synthesis methodology of asymptotic stabilising, energy-based, boundary control laws, that is applicable to a large class of distributed port- Hamiltonian systems. Similarly to the finite dimensional case, the idea is to design a state feedback law able to perform the energy-shaping task, i.e. able to map the open-loop port- Hamiltonian system into a new one in the same form, but characterised by a new Hamiltonian with a unique and isolated minimum at the equilibrium. Asymptotic stability is then obtained via damping injection on the boundary, and is a consequence of the La Salle’s Invariance Principle in infinite dimensions. The general theory is illustrated with the help of a simple concluding example, i.e. the boundary stabilisation of a transmission line with distributed dissipation.

Keywords

distributed port-Hamiltonian systems; boundary control; energy-shaping control; stability of PDEs

Citation

• Journal: IFAC-PapersOnLine
• Year: 2015
• Volume: 48
• Issue: 1
• Pages: 488–493
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2015.05.143
• Note: 8th Vienna International Conferenceon Mathematical Modelling- MATHMOD 2015

BibTeX

@article{Macchelli_2015,
  title={{Asymptotic Stabilisation of Distributed Port-Hamiltonian Systems by Boundary Energy-Shaping Control}},
  volume={48},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2015.05.143},
  number={1},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Macchelli, Alessandro and Gorrec, Yann Le and Ramirez, Héctor},
  year={2015},
  pages={488--493}
}

Download the bib file

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