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Synchronization of the unified chaotic systems using a sliding mode controller

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  • Zribi, Mohamed
  • Smaoui, Nejib
  • Salim, Haitham

Abstract

The unified chaotic system incorporates the behaviors of the Lorenz, the Chen and the Lü chaotic systems. This paper deals with the synchronization of two identical unified chaotic systems where the slave system is assumed to have a single input. A sliding mode controller is proposed to synchronize the two systems. The asymptotic convergence to zero of the errors between the states of the master and the slave systems is shown. Simulations results are presented to illustrate the proposed controller; they indicate that the designed controller is able to synchronize the unified chaotic systems. Also, simulation results show that the proposed control scheme is robust to random bounded disturbances acting on the master system. Moreover, the proposed scheme is applied to the secure communications field, where simulation results indicate that the proposed scheme is effective.

Suggested Citation

  • Zribi, Mohamed & Smaoui, Nejib & Salim, Haitham, 2009. "Synchronization of the unified chaotic systems using a sliding mode controller," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3197-3209.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:3197-3209
    DOI: 10.1016/j.chaos.2009.04.051
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    5. Chen, Heng-Hui & Lee, Ching-I & Yang, Pao-Hwa, 2009. "Adaptive synchronization of linearly coupled unified chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 598-606.
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    9. Uçar, Ahmet & Lonngren, Karl E. & Bai, Er-Wei, 2006. "Synchronization of the unified chaotic systems via active control," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1292-1297.
    10. 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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    Cited by:

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    3. Soriano-Sánchez, A.G. & Posadas-Castillo, C. & Platas-Garza, M.A. & Cruz-Hernández, C. & López-Gutiérrez, R.M., 2016. "Coupling strength computation for chaotic synchronization of complex networks with multi-scroll attractors," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 305-316.
    4. Yao, Qijia & Alsaade, Fawaz W. & Al-zahrani, Mohammed S. & Jahanshahi, Hadi, 2023. "Fixed-time neural control for output-constrained synchronization of second-order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    5. Soriano-Sánchez, A.G. & Posadas-Castillo, C. & Platas-Garza, M.A. & Diaz-Romero, D.A., 2015. "Performance improvement of chaotic encryption via energy and frequency location criteria," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 112(C), pages 14-27.
    6. Qijia Yao & Hadi Jahanshahi & Stelios Bekiros & Jinping Liu & Abdullah A. Al-Barakati, 2023. "Fixed-Time Adaptive Chaotic Control for Permanent Magnet Synchronous Motor Subject to Unknown Parameters and Perturbations," Mathematics, MDPI, vol. 11(14), pages 1-14, July.
    7. Yao, Qijia, 2021. "Neural adaptive learning synchronization of second-order uncertain chaotic systems with prescribed performance guarantees," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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