Boundary control of distributed port-hamiltonian systems via generalised canonical transformations

Authors

Alessandro Macchelli, Yann Le Gorrec, Hector Ramirez

Abstract

This paper presents a novel approach for the development of boundary control laws for a class of linear, distributed port-Hamiltonian systems, with one dimensional spatial domain. The idea is to determine a control action able to map the initial system into a target one, characterised not only by a different Hamiltonian function, but also by new internal dissipative and power-preserving interconnection structures. The methodology consists of two main steps, each associated to a generalised canonical transformation. In the first one, a coordinate change (based on a combination of a linear mapping and a backstepping transformation) is employed to modify the internal structure of the system. Then, in the second step, a generalised canonical transformation capable of properly shaping the Hamiltonian function is introduced. The proposed approach is illustrated with the help of an example, the boundary stabilisation of a lossless transmission line.

Citation

• Journal: 2017 IEEE 56th Annual Conference on Decision and Control (CDC)
• Year: 2017
• Volume:
• Issue:
• Pages: 70–75
• Publisher: IEEE
• DOI: 10.1109/cdc.2017.8263645

BibTeX

@inproceedings{Macchelli_2017,
  title={{Boundary control of distributed port-hamiltonian systems via generalised canonical transformations}},
  DOI={10.1109/cdc.2017.8263645},
  booktitle={{2017 IEEE 56th Annual Conference on Decision and Control (CDC)}},
  publisher={IEEE},
  author={Macchelli, Alessandro and Le Gorrec, Yann and Ramirez, Hector},
  year={2017},
  pages={70--75}
}

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References

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