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Iterative learning control for differential inclusions of parabolic type with noninstantaneous impulses

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Listed:
  • Liu, Shengda
  • Wang, JinRong
  • Shen, Dong
  • O’Regan, Donal

Abstract

In this paper, we present a numerical solution for a finite time complete tracking problem based on the iterative learning control technique for dynamical systems governed by partial differential inclusions of parabolic type with noninstantaneous impulses. By imposing a standard Lipschitz condition on a set-valued mapping and applying conventional P-type updating laws with an initial iterative learning mechanism, we successfully establish an iterative learning process for the tracking problem and conduct a novel convergence analysis with the help of Steiner-type selectors. Sufficient conditions are presented for ensuring asymptotical convergence of the tracking error to zero. Numerical examples are provided to verify the effectiveness of the proposed method with a suitable selection of set-valued mappings.

Suggested Citation

  • Liu, Shengda & Wang, JinRong & Shen, Dong & O’Regan, Donal, 2019. "Iterative learning control for differential inclusions of parabolic type with noninstantaneous impulses," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 48-59.
    • Handle: RePEc:eee:apmaco:v:350:y:2019:i:c:p:48-59
    DOI: 10.1016/j.amc.2018.12.058
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    References listed on IDEAS

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    1. Yan Li & YangQuan Chen & Hyo-Sung Ahn & Guohui Tian, 2013. "A Survey on Fractional-Order Iterative Learning Control," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 127-140, January.
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    Cited by:

    1. Yu Chen & JinRong Wang, 2019. "Continuous Dependence of Solutions of Integer and Fractional Order Non-Instantaneous Impulsive Equations with Random Impulsive and Junction Points," Mathematics, MDPI, vol. 7(4), pages 1-13, April.

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