Nonlinear Dynamics

, Volume 70, Issue 3, pp 2129–2143 | Cite as

Adaptive synchronization of chaotic systems with unknown parameters via new backstepping strategy

  • Shih-Yu Li
  • Cheng-Hsiung Yang
  • Chin-Teng Lin
  • Li-Wei Ko
  • Tien-Ting Chiu
Original Paper


In this paper, a new effective approach—backstepping with Ge–Yao–Chen (GYC) partial region stability theory (called BGYC in this article) is proposed to applied to adaptive synchronization. Backstepping design is a recursive procedure that combines the choice of a Lyapunov function with the design of a controller, and it presents a systematic procedure for selecting a proper controller in chaos synchronization. We further combine the systematic backstepping design and GYC partial region stability theory in this article, Lyapunov function can be chosen as a simple linear homogeneous function of states, and the controllers and the update laws of parameters shall be much simpler. Further, it also introduces less simulation error—the numerical simulation results show that the states errors and parametric errors approach to zero much more exactly and efficiently, which are compared with the original one. Two cases are presented in the simulation results to show the effectiveness and feasibility of our new strategy.


BGYC Synchronization Chaotic system 



This work was supported in part by the UST-UCSD International Center of Excellence in Advanced Bioengineering sponsored by the Taiwan National Science Council I-RiCE Program under Grant No. NSC-100-2911-I-009-101. This research was supported by the National Science Council, Republic of China, under Grant No. NSC 99-2221-E-009-019.


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Shih-Yu Li
    • 1
    • 2
  • Cheng-Hsiung Yang
    • 3
  • Chin-Teng Lin
    • 2
    • 4
  • Li-Wei Ko
    • 1
    • 2
  • Tien-Ting Chiu
    • 5
  1. 1.Department of Biological Science and TechnologyNational Chiao Tung UniversityHsinchuRepublic of China
  2. 2.Brain Research CenterNational Chiao Tung UniversityHsinchuRepublic of China
  3. 3.Department of Automatic ControlNational Taiwan University of Science and TechnologyTaipei CityRepublic of China
  4. 4.Department of Electrical and Control EngineeringNational Chiao Tung UniversityHsinchuRepublic of China
  5. 5.Department of Industrial and Systems EngineeringChung Yuan Christian UniversityChung-LiRepublic of China

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