Infinite-Dimensional Observers for High-Order Boundary-Controlled Port-Hamiltonian Systems

Authors

Jesus-Pablo Toledo-Zucco, Yongxin Wu, Hector Ramirez, Yann Le Gorrec

Abstract

This letter investigates the design of a class of infinite-dimensional observers for one dimensional (1D) boundary controlled port-Hamiltonian systems (BC-PHS) defined by differential operators of order \( N \geq 1 \). The convergence of the proposed observer depends on the number and location of available boundary measurements. Asymptotic convergence is assured for \( N\geq 1 \), and provided that enough boundary measurements are available, exponential convergence can be assured for the cases \( N=1 \) and \( N=2 \). Furthermore, in the case of partitioned BC-PHS with \( N=2 \), such as the Euler-Bernoulli beam, it is shown that exponential convergence can be assured considering less available measurements. The Euler-Bernoulli beam model is used to illustrate the design of the proposed observers and to perform numerical simulations.

Citation

• Journal: IEEE Control Systems Letters
• Year: 2023
• Volume: 7
• Issue:
• Pages: 1676–1681
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/lcsys.2023.3278252

BibTeX

@article{Toledo_Zucco_2023,
  title={{Infinite-Dimensional Observers for High-Order Boundary-Controlled Port-Hamiltonian Systems}},
  volume={7},
  ISSN={2475-1456},
  DOI={10.1109/lcsys.2023.3278252},
  journal={IEEE Control Systems Letters},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Toledo-Zucco, Jesus-Pablo and Wu, Yongxin and Ramirez, Hector and Le Gorrec, Yann},
  year={2023},
  pages={1676--1681}
}

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