On the control by interconnection and exponential stabilisation of infinite dimensional port-Hamiltonian systems

Authors

Alessandro Macchelli

Abstract

This paper aims at illustrating how the control by interconnection methodology (energy-Casimir method) can be employed in the development of exponentially stabilising boundary control laws for a class of linear, distributed port-Hamiltonian systems with one dimensional spatial domain. The energy-Casimir method is the starting point to determine a state-feedback law able to shape the closed-loop Hamiltonian and achieve simple stability. Then, it is shown how to design a further control loop that guarantees exponential convergence. Thanks to this result, it is possible to overcome a limitation of standard damping injection strategies that, if combined with energy shaping control laws based on energy-balancing, are able to assure, in general, only asymptotic convergence. The methodology is illustrated with the help of a simple example, the boundary stabilisation of a lossless transmission line.

Citation

• Journal: 2016 IEEE 55th Conference on Decision and Control (CDC)
• Year: 2016
• Volume:
• Issue:
• Pages: 3137–3142
• Publisher: IEEE
• DOI: 10.1109/cdc.2016.7798739

BibTeX

@inproceedings{Macchelli_2016,
  title={{On the control by interconnection and exponential stabilisation of infinite dimensional port-Hamiltonian systems}},
  DOI={10.1109/cdc.2016.7798739},
  booktitle={{2016 IEEE 55th Conference on Decision and Control (CDC)}},
  publisher={IEEE},
  author={Macchelli, Alessandro},
  year={2016},
  pages={3137--3142}
}

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