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Adaptive fuzzy sliding mode control for synchronization of uncertain fractional order chaotic systems

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  • Lin, Tsung-Chih
  • Lee, Tun-Yuan
  • Balas, Valentina E.

Abstract

This paper deals with chaos synchronization between two different uncertain fractional order chaotic systems based on adaptive fuzzy sliding mode control (AFSMC). With the definition of fractional derivatives and integrals, a fuzzy Lyapunov synthesis approach is proposed to tune free parameters of the adaptive fuzzy controller on line by output feedback control law and adaptive law. Moreover, chattering phenomena in the control efforts can be reduced. The sliding mode design procedure not only guarantees the stability and robustness of the proposed AFSMC, but also the external disturbance on the synchronization error can be attenuated. The simulation example is included to confirm validity and synchronization performance of the advocated design methodology.

Suggested Citation

  • Lin, Tsung-Chih & Lee, Tun-Yuan & Balas, Valentina E., 2011. "Adaptive fuzzy sliding mode control for synchronization of uncertain fractional order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 791-801.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:10:p:791-801
    DOI: 10.1016/j.chaos.2011.04.005
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    References listed on IDEAS

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    1. Lu, Jun Guo & Chen, Guanrong, 2006. "A note on the fractional-order Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 685-688.
    2. Deng, W.H. & Li, C.P., 2005. "Chaos synchronization of the fractional Lü system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 61-72.
    3. Gao, Xin & Yu, Juebang, 2005. "Chaos in the fractional order periodically forced complex Duffing’s oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1097-1104.
    4. Zhou, Shangbo & Li, Hua & Zhu, Zhengzhou, 2008. "Chaos control and synchronization in a fractional neuron network system," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 973-984.
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    Cited by:

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    2. Xia, Yude & Wang, Jing & Meng, Bo & Chen, Xiangyong, 2020. "Further results on fuzzy sampled-data stabilization of chaotic nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 379(C).
    3. Deepika, Deepika & Kaur, Sandeep & Narayan, Shiv, 2018. "Uncertainty and disturbance estimator based robust synchronization for a class of uncertain fractional chaotic system via fractional order sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 196-203.
    4. Gao, Yuan & Liang, Chenghua & Wu, Qiqi & Yuan, Haiying, 2015. "A new fractional-order hyperchaotic system and its modified projective synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 190-204.
    5. Balootaki, Mohammad Ahmadi & Rahmani, Hossein & Moeinkhah, Hossein & Mohammadzadeh, Ardashir, 2020. "On the Synchronization and Stabilization of fractional-order chaotic systems: Recent advances and future perspectives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    6. Chih-Hsueh Lin & Guo-Hsin Hu & Jun-Juh Yan, 2021. "Estimation of Synchronization Errors between Master and Slave Chaotic Systems with Matched/Mismatched Disturbances and Input Uncertainty," Mathematics, MDPI, vol. 9(2), pages 1-15, January.
    7. Jian, Huan-Yan & Huang, Ting-Zhu & Ostermann, Alexander & Gu, Xian-Ming & Zhao, Yong-Liang, 2021. "Fast numerical schemes for nonlinear space-fractional multidelay reaction-diffusion equations by implicit integration factor methods," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    8. Leng, Xiangxin & Gu, Shuangquan & Peng, Qiqi & Du, Baoxiang, 2021. "Study on a four-dimensional fractional-order system with dissipative and conservative properties," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    9. Yousefpour, Amin & Jahanshahi, Hadi & Munoz-Pacheco, Jesus M. & Bekiros, Stelios & Wei, Zhouchao, 2020. "A fractional-order hyper-chaotic economic system with transient chaos," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).

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