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High-Order \(\mathcal{D}^{\alpha}\)-Type Iterative Learning Control for Fractional-Order Nonlinear Time-Delay Systems

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Abstract

This paper presents a high-order \(\mathcal{D}^{\alpha}\)-type iterative learning control (ILC) scheme for a class of fractional-order nonlinear time-delay systems. First, a discrete system for \(\mathcal{D}^{\alpha}\)-type ILC is established by analyzing the control and learning processes, and the ILC design problem is then converted to a stabilization problem for this discrete system. Next, by introducing a suitable norm and using a generalized Gronwall–Bellman Lemma, the sufficiency condition for the robust convergence with respect to the bounded external disturbance of the control input and the tracking errors is obtained. Finally, the validity of the method is verified by a numerical example.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of P.R. China (61104072, 10971173).

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Authors and Affiliations

  1. Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Hunan, 411105, P.R. China

    Yong-Hong Lan

  2. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, 411105, P.R. China

    Yong Zhou

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  1. Yong-Hong Lan
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  2. Yong Zhou
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Correspondence to Yong Zhou.

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Lan, YH., Zhou, Y. High-Order \(\mathcal{D}^{\alpha}\)-Type Iterative Learning Control for Fractional-Order Nonlinear Time-Delay Systems. J Optim Theory Appl 156, 153–166 (2013). https://doi.org/10.1007/s10957-012-0231-2

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  • DOI: https://doi.org/10.1007/s10957-012-0231-2

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