Distributed-Parameter Port-Hamiltonian Systems in Discrete-Time

Authors

Abstract

This paper presents a design framework of discrete-time regulators for linear, port-Hamiltonian, boundary control systems. The contribution is twofold. At first, a discrete-time approximation of the plant dynamics originally described by a linear PDE with boundary actuation is introduced. The discretisation is performed in time only. Thus, the “distributed nature” of the state is maintained. Such a system inherits the passivity of the original one and is well-posed, namely the “next” state always exists. The second result is the characterisation of discrete-time, linear controllers in the port-Hamiltonian form that render the closed-loop dynamics asymptotically stable. A numerical example illustrates the effectiveness of the proposed framework.

Citation

Journal: 2023 62nd IEEE Conference on Decision and Control (CDC)
Year: 2023
Volume:
Issue:
Pages: 2931–2936
Publisher: IEEE
DOI: 10.1109/cdc49753.2023.10383674

BibTeX

@inproceedings{Macchelli_2023,
  title={{Distributed-Parameter Port-Hamiltonian Systems in Discrete-Time}},
  DOI={10.1109/cdc49753.2023.10383674},
  booktitle={{2023 62nd IEEE Conference on Decision and Control (CDC)}},
  publisher={IEEE},
  author={Macchelli, Alessandro},
  year={2023},
  pages={2931--2936}
}

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