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Controlling and tracking hyperchaotic Rössler system via active backstepping design

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  • Zhang, Hao
  • Ma, Xi-kui
  • Li, Ming
  • Zou, Jian-long

Abstract

This paper presents a novel active backstepping control approach for controlling hyperchaotic Rössler system to a steady state as well as tracking of any desire trajectory to be achieved in a systematic way. The proposed method is a systematic design approach and consists in a recursive procedure that interlaces the choice of a Lyapunov function with the design of active control. Numerical results show that the controller is singularity free and the closed-loop system is stable globally. Especially, the main feature of this technique is that it gives the flexibility to construct a control law. Finally, numerical experiments verify the feasibility and effectiveness of the proposed control technique.

Suggested Citation

  • Zhang, Hao & Ma, Xi-kui & Li, Ming & Zou, Jian-long, 2005. "Controlling and tracking hyperchaotic Rössler system via active backstepping design," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 353-361.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:2:p:353-361
    DOI: 10.1016/j.chaos.2004.12.032
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    Citations

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    Cited by:

    1. Feki, Moez, 2009. "Sliding mode control and synchronization of chaotic systems with parametric uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1390-1400.
    2. Zhou, Xiaobing & Wu, Yue & Li, Yi & Xue, Hongquan, 2009. "Adaptive control and synchronization of a new modified hyperchaotic Lü system with uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2477-2483.
    3. Li, Guo-Hui, 2007. "Generalized projective synchronization between Lorenz system and Chen’s system," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1454-1458.
    4. Wang, Xingyuan & Wang, Mingjun, 2008. "A hyperchaos generated from Lorenz system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3751-3758.
    5. Al-Sawalha, M. Mossa & Noorani, M.S.M. & Hashim, I., 2009. "On accuracy of Adomian decomposition method for hyperchaotic Rössler system," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1801-1807.

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