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Universal function projective lag synchronization of chaotic systems with uncertainty by using active sliding mode and fuzzy sliding mode control

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Abstract

In this paper, a novel synchronization scheme, universal function projective lag synchronization (UFPLS), is proposed. The synchronization scheme is a generalization of universal function projective synchronization and modified function projective lag synchronization. An active sliding mode controller is introduced for UFPLS of chaotic systems. By using the integral sliding surface, the determination of sliding parameters become easier than using the classical one. Furthermore, based on the consideration of reality, the systems with uncertainty and the system contaminated by noise are investigated. Theoretical proof is achieved with the Lyapunov stability theory. A fuzzy active sliding control method is presented by using a fuzzy system to adjust the coefficient of switch term so that the chattering can be weakened. Simulation results verify the effectiveness of the introduced schemes and illustrate that the application of fuzzy system eliminates the chattering effectively.

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Acknowledgments

This work is supported partly by National Natural Science Foundation of China (Grant No. 61374118), Natural Science Foundation of Yunnan Province (Grant No. 2013FZ113), Yunnan Province Education Department Scientific Research Fund Project (Grant No. 2014Y441). Science and Technology Research Foundation of Education Bureau of Heilongjiang Province, China (Grant No. 12543065).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Qujing Normal University, Qujing, 655011, China

    Baojie Zhang

  2. Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024, China

    Baojie Zhang

  3. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023, China

    Haigang Guo

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  1. Baojie Zhang
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  2. Haigang Guo
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Zhang, B., Guo, H. Universal function projective lag synchronization of chaotic systems with uncertainty by using active sliding mode and fuzzy sliding mode control. Nonlinear Dyn 81, 867–879 (2015). https://doi.org/10.1007/s11071-015-2036-y

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