Neural Energy Casimir Control for Port-Hamiltonian Systems

Authors

Liang Xu, Muhammad Zakwan, Giancarlo Ferrari-Trecate

Abstract

The energy Casimir method is an effective controller design approach to stabilize port-Hamiltonian systems at a desired equilibrium. However, its application relies on the availability of suitable Casimir and Lyapunov functions, whose computation are generally intractable. In this paper, we propose a neural network-based framework to learn these functions. We show how to achieve equilibrium assignment by adding suitable regularization terms in the training cost. We also propose a parameterization of Casimir functions for reducing the training complexity. Moreover, the distance between the equilibrium of the learned Lyapunov function and the desired equilibrium is analyzed, which indicates that for small suboptimality gaps, the distance decreases linearly with respect to the training loss. Our methods are backed up by simulations on a pendulum system.

Citation

Journal: 2022 IEEE 61st Conference on Decision and Control (CDC)
Year: 2022
Volume:
Issue:
Pages: 4053–4058
Publisher: IEEE
DOI: 10.1109/cdc51059.2022.9992784

BibTeX

@inproceedings{Xu_2022,
  title={{Neural Energy Casimir Control for Port-Hamiltonian Systems}},
  DOI={10.1109/cdc51059.2022.9992784},
  booktitle={{2022 IEEE 61st Conference on Decision and Control (CDC)}},
  publisher={IEEE},
  author={Xu, Liang and Zakwan, Muhammad and Ferrari-Trecate, Giancarlo},
  year={2022},
  pages={4053--4058}
}

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