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Reduced‐Order Antisynchronization of Chaotic Systems via Adaptive Sliding Mode Control

Author

Listed:
  • Wafaa Jawaada
  • M. S. M. Noorani
  • M. Mossa Al-Sawalha
  • M. Abdul Majid

Abstract

A novel reduced‐order adaptive sliding mode controller is developed and experimented in this paper to antisynchronize two different chaotic systems with different order. Based upon the parameters modulation and the adaptive sliding mode control techniques, we show that dynamical evolution of third‐order chaotic system can be antisynchronized with the projection of a fourth‐order chaotic system even though their parameters are unknown. The techniques are successfully applied to two examples: firstly Lorenz (4th‐order) and Lorenz (3rd‐order) and secondly the hyperchaotic Lü (4th‐order) and Chen (3rd‐order). Theoretical analysis and numerical simulations are shown to verify the results.

Suggested Citation

  • Wafaa Jawaada & M. S. M. Noorani & M. Mossa Al-Sawalha & M. Abdul Majid, 2013. "Reduced‐Order Antisynchronization of Chaotic Systems via Adaptive Sliding Mode Control," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:415652
    DOI: 10.1155/2013/415652
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    References listed on IDEAS

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    1. Chen, Aimin & Lu, Junan & Lü, Jinhu & Yu, Simin, 2006. "Generating hyperchaotic Lü attractor via state feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 103-110.
    2. Cao, Jinde & Wang, Zidong & Sun, Yonghui, 2007. "Synchronization in an array of linearly stochastically coupled networks with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 718-728.
    3. Zhang, Qunjiao & Lu, Jun-an, 2008. "Chaos synchronization of a new chaotic system via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 175-179.
    4. Yan, Jun-Juh & Yang, Yi-Sung & Chiang, Tsung-Ying & Chen, Ching-Yuan, 2007. "Robust synchronization of unified chaotic systems via sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 947-954.
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