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Finite-time combination-combination synchronization of four different chaotic systems with unknown parameters via sliding mode control

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Abstract

In this paper, we apply the nonsingular terminal sliding mode control technique to realize the novel combination-combination synchronization between combination of two chaotic systems as drive system and combination of two chaotic systems as response system with unknown parameters in a finite time. On the basic of the adaptive laws and finite-time stability theory, an adaptive combination sliding mode controller is proposed to ensure the occurrence of the sliding motion in a given finite time for four different chaotic systems. In theory, it is proved that the sliding mode technique can realize fast convergence for four different chaotic systems in the finite time. Some criteria and corollaries are derived for finite-time combination-combination synchronization of four different chaotic systems. Numerical simulation results are shown to verify the effectiveness and correctness of the combination-combination synchronization.

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Acknowledgements

The authors thank the editor and the anonymous reviewers for their resourceful and valuable comments and constructive suggestions. This project is supported by the State Key Program of the National Natural Science Foundation of China (Grant No. 61134012), the National Natural Science Foundation of China (Grant Nos. 11271146, 61374150), the Fundamental Research Funds for the Central Universities (HUST: 2013TS126), and the Science and Technology Program of Wuhan (Grant No. 20130105010117) the Doctoral Fund of Ministry of Education of China (Grant No. 20130142130012).

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Authors and Affiliations

  1. School of Automation, Huazhong University of Science and Technology, Hubei, 430074, China

    Junwei Sun, Yi Shen, Xiaoping Wang & Jie Chen

  2. Key Laboratory of Ministry of Education for Image Processing and Intelligent Control, Huazhong University of Science and Technology, Hubei, 430074, China

    Junwei Sun, Yi Shen, Xiaoping Wang & Jie Chen

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  1. Junwei Sun
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  2. Yi Shen
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  3. Xiaoping Wang
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  4. Jie Chen
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Correspondence to Junwei Sun.

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Sun, J., Shen, Y., Wang, X. et al. Finite-time combination-combination synchronization of four different chaotic systems with unknown parameters via sliding mode control. Nonlinear Dyn 76, 383–397 (2014). https://doi.org/10.1007/s11071-013-1133-z

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  • DOI: https://doi.org/10.1007/s11071-013-1133-z

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