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Complete (anti-)synchronization of chaotic systems with fully uncertain parameters by adaptive control

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Abstract

This paper addresses a unified mathematical expression describing a class of chaotic systems, for which the problem of synchronization and anti-synchronization between different chaotic systems with fully uncertain parameters and different structure are studied. Based on the Lyapunov stability theory, a novel, simple, and systemic adaptive synchronization controller is designated, the analytic expression of the controller and the adaptive laws of parameters are developed. Moreover, the proposed scheme can be extended to anti-synchronize a class of chaotic systems. Two chaotic systems with different structure and fully uncertain parameters are employed as the examples to show the effectiveness of the proposed adaptive synchronization and anti-synchronization schemes. Additionally, the robustness and noise immunity of the adaptive synchronization scheme is investigated by measuring the mean squared error of the systems.

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Authors and Affiliations

  1. Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, 730070, China

    Xian-Feng Li & Yan-Dong Chu

  2. Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China

    Andrew Chi-Sing Leung

  3. School of Mathematical Sciences, Shandong Normal University, Jinan, 250014, China

    Xiu-Ping Han

  4. Department of Mathematics, Tianshui Normal College, Tianshui, China

    Xiao-Jun Liu

Authors
  1. Xian-Feng Li
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  2. Andrew Chi-Sing Leung
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  3. Xiu-Ping Han
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  4. Xiao-Jun Liu
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  5. Yan-Dong Chu
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Correspondence to Xian-Feng Li.

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Li, XF., Leung, A.CS., Han, XP. et al. Complete (anti-)synchronization of chaotic systems with fully uncertain parameters by adaptive control. Nonlinear Dyn 63, 263–275 (2011). https://doi.org/10.1007/s11071-010-9802-7

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  • DOI: https://doi.org/10.1007/s11071-010-9802-7

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