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Estimation of Synchronization Errors between Master and Slave Chaotic Systems with Matched/Mismatched Disturbances and Input Uncertainty

Author

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  • Chih-Hsueh Lin

    (Department of Electronic Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 80778, Taiwan)

  • Guo-Hsin Hu

    (Department of Electronic Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 80778, Taiwan
    Department of Industrial Upgrading Service, Metal Industries Research & Development Centre, Kaohsiung 81160, Taiwan)

  • Jun-Juh Yan

    (Department of Electronic Engineering, National Chin-Yi University of Technology, Taichung 41107, Taiwan)

Abstract

This study is concerned with robust synchronization for master–slave chaotic systems with matched/mismatched disturbances and uncertainty in the control input. A robust sliding mode control (SMC) is presented to achieve chaos synchronization even under the influence of matched/mismatched disturbances and uncertainty of inputs. A proportional-integral (PI) switching surface is introduced to make the controlled error dynamics in the sliding manifold easy to analyze. Furthermore, by using the proposed SMC scheme even subjected to input uncertainty, we can force the trajectories of the error dynamics to enter the sliding manifold and fully synchronize the master–slave systems in spite of matched uncertainties and input nonlinearity. As for the mismatched disturbances, the bounds of synchronization errors can be well estimated by introducing the limit of the Riemann sum, which is not well addressed in previous works. Simulation experiments including matched and mismatched cases are presented to illustrate the robustness and synchronization performance with the proposed SMC synchronization controller.

Suggested Citation

  • Chih-Hsueh Lin & Guo-Hsin Hu & Jun-Juh Yan, 2021. "Estimation of Synchronization Errors between Master and Slave Chaotic Systems with Matched/Mismatched Disturbances and Input Uncertainty," Mathematics, MDPI, vol. 9(2), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:176-:d:481851
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    References listed on IDEAS

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    1. Haiyun Zhang & Deyuan Meng & Jin Wang & Guodong Lu, 2020. "Synchronisation of uncertain chaotic systems via fuzzy-regulated adaptive optimal control approach," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(3), pages 473-487, February.
    2. Chi-Hsin Yang & Kun-Chieh Wang & Long Wu & Ren Wen, 2020. "State Synchronization for a Class of n -Dimensional Nonlinear Systems with Sector Input Nonlinearity via Adaptive Two-Stage Sliding Mode Control," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-11, July.
    3. Lin, Tsung-Chih & Lee, Tun-Yuan & Balas, Valentina E., 2011. "Adaptive fuzzy sliding mode control for synchronization of uncertain fractional order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 791-801.
    4. Dadras, Sara & Momeni, Hamid Reza, 2010. "Adaptive sliding mode control of chaotic dynamical systems with application to synchronization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(12), pages 2245-2257.
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    Cited by:

    1. Ruizhi Sha & Zuren Feng, 2023. "A Sliding Mode Control Algorithm with Elementary Compensation for Input Matrix Uncertainty in Affine Systems," Mathematics, MDPI, vol. 11(6), pages 1-23, March.

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