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Learning ability analysis for linear discrete delay systems with iteration-varying trial length

Author

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  • Luo, Hongwei
  • Wang, JinRong
  • Shen, Dong

Abstract

This study investigates finite-time tracking issues of linear discrete delay systems with iteration-varying trial length (IVTL). With the assistance of explicit solutions expressed by the discrete matrix delayed exponential emA⋅, the obstacle in explicitly expressing the tracking error is overcome. Iterative learning control (ILC) update laws using the current state feedback control are proposed to reduce greatly acute error jitter caused by IVTL. The convergence conditions are presented for realizable systems and learning ability of the delay systems. The relation between ‖emA⋅‖1 and probability distribution of the trial length is given to imply how to guarantee convergence of tracking error. Finally, a numerical simulation is presented to illustrate that the ILC scheme can improve transient tracking performance. Moreover, convergence speed of the delay systems can be expedited.

Suggested Citation

  • Luo, Hongwei & Wang, JinRong & Shen, Dong, 2023. "Learning ability analysis for linear discrete delay systems with iteration-varying trial length," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:chsofr:v:171:y:2023:i:c:s0960077923003296
    DOI: 10.1016/j.chaos.2023.113428
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    References listed on IDEAS

    as
    1. Yamiao Zhang & Jian Liu & Xiaoe Ruan, 2022. "Learning ability of iterative learning control system with a randomly varying trial length," International Journal of Systems Science, Taylor & Francis Journals, vol. 53(4), pages 870-882, March.
    2. Yong-Hong Lan & Yong Zhou, 2013. "High-Order $\mathcal{D}^{\alpha}$ -Type Iterative Learning Control for Fractional-Order Nonlinear Time-Delay Systems," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 153-166, January.
    3. Jian Liu & Yamiao Zhang & Xiaoe Ruan, 2019. "Iterative learning control for a class of uncertain nonlinear systems with current state feedback," International Journal of Systems Science, Taylor & Francis Journals, vol. 50(10), pages 1889-1901, July.
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