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Convergence Analysis for Iterative Learning Control of Conformable Impulsive Differential Equations

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Abstract

This paper deals with iterative learning control for conformable impulsive differential equations. For nonlinear and linear problems varying with the initial state, we design standard P-type, \(D_{\gamma }\)-type, and conformable \(PI_{\gamma }D_{\gamma }\)-type learning update laws. Next, we establish sufficient conditions for tracking error convergence and use impulsive Gronwall inequality and mathematical analysis tools to prove the main results. Finally, three numerical examples are given to illustrate our theoretical results.

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Acknowledgements

The authors are grateful to the referees for their careful reading of the manuscript and their valuable comments.

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Authors and Affiliations

  1. Department of Mathematics, Guizhou University, Guiyang, 550025, Guizhou, China

    Wanzheng Qiu & JinRong Wang

  2. Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48, Bratislava, Slovakia

    Michal Fečkan

  3. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Michal Fečkan

  4. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

    Donal O’Regan

  5. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, China

    JinRong Wang

Authors
  1. Wanzheng Qiu
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  2. Michal Fečkan
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  3. Donal O’Regan
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  4. JinRong Wang
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Correspondence to JinRong Wang.

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Communicated by Davoud Mirzaei.

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This work is partially supported by the National Natural Science Foundation of China (11661016), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006), Major Research Project of Innovative Group in Guizhou Education Department ([2018]012), Guizhou Data Driven Modeling Learning and Optimization Innovation Team ([2020]5016), the Slovak Research and Development Agency under the contract No. APVV-18-0308, and the Slovak Grant Agency VEGA No. 1/0358/20 and No. 2/0127/20.

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Qiu, W., Fečkan, M., O’Regan, D. et al. Convergence Analysis for Iterative Learning Control of Conformable Impulsive Differential Equations. Bull. Iran. Math. Soc. 48, 193–212 (2022). https://doi.org/10.1007/s41980-020-00510-6

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  • DOI: https://doi.org/10.1007/s41980-020-00510-6

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