Port-representation of bi-Hamiltonian structure for infinite-dimensional symmetry

Authors

null Gou Nishida, null Masaki Yamakita, null Zhi-wei Luo

Abstract

In this paper, the port-representation of conservation laws is extended to a wider class of symmetries, the infinite-dimensional symmetry expressed by the bi-Hamiltonian system. It is known from Noether’s theorem that a conservation law is associated with an invariant property called a symmetry. In certain cases, the symmetry appears in a system as a hidden infinite-dimensional structure. Such a structure can be defined by using a recursive operator consisting of a Hamiltonian pair and is called a bi-Hamiltonian structure. The bi-Hamiltonian structure induces a hierarchical set of conservation laws. This concept can be used for reducing a system possessing a bi-Hamiltonian structure to simpler port-representations of the conservation laws. Finally, a boundary observer for symmetry destruction is shown.

Citation

• Journal: 2007 46th IEEE Conference on Decision and Control
• Year: 2007
• Volume:
• Issue:
• Pages: 5588–5593
• Publisher: IEEE
• DOI: 10.1109/cdc.2007.4434262

BibTeX

@inproceedings{Gou_Nishida_2007,
  title={{Port-representation of bi-Hamiltonian structure for infinite-dimensional symmetry}},
  DOI={10.1109/cdc.2007.4434262},
  booktitle={{2007 46th IEEE Conference on Decision and Control}},
  publisher={IEEE},
  author={Gou Nishida and Masaki Yamakita and Zhi-wei Luo},
  year={2007},
  pages={5588--5593}
}

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