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Hybrid function projective synchronization of chaotic systems with uncertain time-varying parameters via Fourier series expansion

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Abstract

In this paper, the hybrid function projective synchronization (HFPS) of different chaotic systems with uncertain periodically time-varying parameters is carried out by Fourier series expansion and adaptive bounding technique. Fourier series expansion is used to deal with uncertain periodically time-varying parameters. Adaptive bounding technique is used to compensate the bound of truncation errors. Using the Lyapunov stability theory, an adaptive control law and six parameter updating laws are constructed to make the states of two different chaotic systems asymptotically synchronized. The control strategy does not need to know the parameters thoroughly if the time-varying parameters are periodical functions. Finally, in order to verify the effectiveness of the proposed scheme, the HFPS between Lorenz system and Chen system is completed successfully by using this scheme.

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Authors and Affiliations

  1. Department of Applied Mathematics, Xidian University, Xi’an, 710071, China

    Chun-Li Zhang & Jun-Min Li

Authors
  1. Chun-Li Zhang
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  2. Jun-Min Li
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Corresponding author

Correspondence to Chun-Li Zhang.

Additional information

This work was supported by National Natural Science Foundation of China (No. 60974139) and Fundamental Research Funds for the Central Universities (No. 72103676).

Chun-Li Zhang graduated from Linyi Normal University, China in 2007. She received the M. Sc. degree from Xidian University in 2010. She is currently a ph.D. candidate at Department of Applied Mathematics, Xidian University.

Her research interests include adaptive iterative learning control, neural network, robust control and chaos synchronization.

Jun-Min Li graduated from Xidian University, China in 1987. He received the M. Sc. degree from Xidian University in 1990 and the Ph.D. degree from the Xi’an Jiao Tong University, China in 1997. He is currently a professor at Department of Applied Mathematics, Xidian University.

His research interests include adaptive control, learning control, intelligent control, hybrid system control theory and the networked control systems, etc.

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Zhang, CL., Li, JM. Hybrid function projective synchronization of chaotic systems with uncertain time-varying parameters via Fourier series expansion. Int. J. Autom. Comput. 9, 388–394 (2012). https://doi.org/10.1007/s11633-012-0659-8

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  • DOI: https://doi.org/10.1007/s11633-012-0659-8

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