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Data-driven gradient-based point-to-point iterative learning control for nonlinear systems

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Abstract

Iterative learning control (ILC) is a well-established methodology which has proved successful in achieving accurate tracking control for repeated tasks. However, the majority of ILC algorithms require a nominal plant model and are sensitive to modelling mismatch. This paper focuses on the class of gradient-based ILC algorithms and proposes a data-driven ILC implementation applicable to a general class of nonlinear systems, in which an explicit model of the plant dynamics is not required. The update of the control signal is generated by an additional experiment executed between ILC trials. The framework is further extended by allowing only specific reference points to be tracked, thereby enabling faster convergence. Necessary convergence conditions and corresponding convergence rates for both approaches are derived theoretically. The proposed data-driven approaches are demonstrated through application to a stroke rehabilitation problem requiring accurate control of nonlinear artificially stimulated muscle dynamics.

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Author information

Authors and Affiliations

  1. School of Electrical Engineering, Zhengzhou University, 100 Science Avenue, Zhengzhou, 450001, Henan, China

    Benyan Huo & Yanghong Liu

  2. School of Electronics and Computer Science, University of Southampton, Southampton, SO17 1BJ, UK

    Chris T. Freeman

Authors
  1. Benyan Huo
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  2. Chris T. Freeman
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  3. Yanghong Liu
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Corresponding author

Correspondence to Yanghong Liu.

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Conflicts of interest

The authors declare that they have no conflict of interest.

Informed consent

Informed consent was obtained from all individual participants included in the study.

Research involving Human Participants

The study is part of a project named ‘A feasibility study using iterative learning control to improve tracking accuracy of functional tasks’ which has been approved by the Faculty of Engineering and Physical Sciences Ethics Committee (FEPS) of University of Southampton, UK. The project is registered on Ethics and Research Governance Online (ERGO) and the Ref number is 47701. Following this protocol, five healthy participants were recruited in this study.

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Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This study was funded by National Natural Science Foundation of China (NO.61473265), the China Postdoctoral Science Foundation (NO.2018M632801) and the ZZU-Southampton Collaborative Research Project under Grant 16306/01. Part of the results in this paper were submitted to 13th IFAC Workshop on Adaptive and Learning Control Systems [1].

Appendix

Appendix

1.1 A. Proof of Proposition 1

Proof

Using Eq. (16),

(58)

\(= \bigtriangledown \varvec{g} ( \hat{\varvec{u}}_{k} )^\top \varvec{e}_k\).

Further, employing the properties of the time reversal operator and combining (58) with (18), we see

(59)

Thus, the gradient ILC update law (20) is obtained.

\(\square \)

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Huo, B., Freeman, C.T. & Liu, Y. Data-driven gradient-based point-to-point iterative learning control for nonlinear systems. Nonlinear Dyn 102, 269–283 (2020). https://doi.org/10.1007/s11071-020-05941-8

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