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Adaptive synchronization of uncertain unified chaotic systems via novel feedback controls

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Abstract

This paper is concerned with the robust adaptive synchronization problem for unified chaotic systems with parameter variation, system uncertainties, and external disturbances. By combining adaptive method and positive time-varying integral functions, novel adaptive synchronization schemes are proposed. It is shown that the synchronization errors between the drive and response chaotic systems converge to zero asymptotically. Finally, illustrative examples about Lorenz chaotic system, Chen chaotic system, and Lü chaotic system are provided to demonstrate the effectiveness and applicability of the proposed design method.

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Acknowledgments

The authors would like to thank the editor and anonymous reviewers for their valuable comments and suggestions. The work of Z. Zhang was supported by the National Natural Science Foundation of China under Grants 61473171, 611 04007, 61273091, and 61374090, China Postdoctoral Science Foundation funded project under Grants 2012M511465 and 2014T70622, and Shandong Postdoctoral Science Foundation funded project under Grant 201203031. Also, the work of J.H. Park was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2013R1A1A2A10005201).

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Authors and Affiliations

  1. School of Engineering, Qufu Normal University, Rizhao, 276826, People’s Republic of China

    Zhengqiang Zhang & Hanyong Shao

  2. Department of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan, 712-749, Republic of Korea

    Zhengqiang Zhang & Ju H. Park

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  1. Zhengqiang Zhang
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  2. Ju H. Park
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  3. Hanyong Shao
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Correspondence to Ju H. Park.

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Zhang, Z., Park, J.H. & Shao, H. Adaptive synchronization of uncertain unified chaotic systems via novel feedback controls. Nonlinear Dyn 81, 695–706 (2015). https://doi.org/10.1007/s11071-015-2020-6

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