Stability Analysis of Nonlinear Repetitive Control Schemes

Authors

Federico Califano, Michelangelo Bin, Alessandro Macchelli, Claudio Melchiorri

Abstract

This letter deals with nonlinear repetitive control (RC), a technique used to reject periodic disturbances with a known and constant period. Since RC systems are defined over a state space of infinite dimension, the main theoretical problem that makes nonlinear case not trivial resides in the lack of adequate mathematical tools to study well-posedness of the closed-loop system and regularity of the solutions. Here, the stability analysis relies on recent results about the boundary control of infinite-dimensional port-Hamiltonian systems via nonlinear regulators, and the major contribution is the definition of a class of nonlinear plants for which a RC scheme is, at first, well-posed, and then exponentially stable. Moreover, an explicit proof of perfect local asymptotic tracking and disturbance rejection for exponentially stable RC systems is provided.

Citation

• Journal: IEEE Control Systems Letters
• Year: 2018
• Volume: 2
• Issue: 4
• Pages: 773–778
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/lcsys.2018.2849617

BibTeX

@article{Califano_2018,
  title={{Stability Analysis of Nonlinear Repetitive Control Schemes}},
  volume={2},
  ISSN={2475-1456},
  DOI={10.1109/lcsys.2018.2849617},
  number={4},
  journal={IEEE Control Systems Letters},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Califano, Federico and Bin, Michelangelo and Macchelli, Alessandro and Melchiorri, Claudio},
  year={2018},
  pages={773--778}
}

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References

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