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Sliding mode synchronization of multiple chaotic systems with uncertainties and disturbances

Author

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  • Chen, Xiangyong
  • Park, Ju H.
  • Cao, Jinde
  • Qiu, Jianlong

Abstract

This paper investigates two classes of synchronization problems of multiple chaotic systems with unknown uncertainties and disturbances by employing sliding mode control. Modified projective synchronization and transmission synchronization are discussed here. For the modified projective synchronization problem, sliding mode controllers are designed to ensure that multiple response systems synchronize with one drive system under the effects of external disturbances. For the transmission synchronization problem, based on adaptive sliding mode control, an integral sliding surface is selected and the adaptive laws are derived to tackle unknown uncertainties and disturbances for such systems. A class of nonlinear adaptive sliding mode controllers is developed to guarantee asymptotical stability of the error systems so that all chaotic systems can synchronize with each other. Simulation results are given to illustrate the effectiveness of the proposed schemes by comparing with the existing methods.

Suggested Citation

  • Chen, Xiangyong & Park, Ju H. & Cao, Jinde & Qiu, Jianlong, 2017. "Sliding mode synchronization of multiple chaotic systems with uncertainties and disturbances," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 161-173.
    • Handle: RePEc:eee:apmaco:v:308:y:2017:i:c:p:161-173
    DOI: 10.1016/j.amc.2017.03.032
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    References listed on IDEAS

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    1. Park, Ju H., 2007. "Adaptive modified projective synchronization of a unified chaotic system with an uncertain parameter," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1552-1559.
    2. Sun, Junwei & Guo, Jinchao & Yang, Cunxiang & Zheng, Anping & Zhang, Xuncai, 2015. "Adaptive generalized hybrid function projective dislocated synchronization of new four-dimensional uncertain chaotic systems," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 304-314.
    3. Zhang, Xuxi & Liu, Xianping & Zhu, Qidan, 2014. "Adaptive chatter free sliding mode control for a class of uncertain chaotic systems," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 431-435.
    4. Pai, Ming-Chang, 2015. "Chaotic sliding mode controllers for uncertain time-delay chaotic systems with input nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 757-767.
    5. Ran, Suzhen & Xue, Yanmei & Zheng, Bo-Chao & Wang, Zhenyou, 2017. "Quantized feedback fuzzy sliding mode control design via memory-based strategy," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 283-295.
    6. Leung, Andrew Y.T. & Li, Xian-Feng & Chu, Yan-Dong & Rao, Xiao-Bo, 2015. "A simple adaptive-feedback scheme for identical synchronizing chaotic systems with uncertain parameters," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 172-183.
    7. Xiangyong Chen & Chengyong Wang & Jianlong Qiu, 2014. "Synchronization and anti-synchronization ofNdifferent coupled chaotic systems with ring connection," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 25(05), pages 1-12.
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