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Adaptive synchronization of fractional Lorenz systems using a reduced number of control signals and parameters

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  • Aguila-Camacho, Norelys
  • Duarte-Mermoud, Manuel A.
  • Delgado-Aguilera, Efredy

Abstract

This paper analyzes the synchronization of two fractional Lorenz systems in two cases: the first one considering fractional Lorenz systems with unknown parameters, and the second one considering known upper bounds on some of the fractional Lorenz systems parameters. The proposed control strategies use a reduced number of control signals and control parameters, employing mild assumptions. The stability of the synchronization errors is analytically demonstrated in all cases, and the convergence to zero of the synchronization errors is analytically proved in the case when the upper bounds on some system parameters are assumed to be known. Simulation studies are presented, which allows verifying the effectiveness of the proposed control strategies.

Suggested Citation

  • Aguila-Camacho, Norelys & Duarte-Mermoud, Manuel A. & Delgado-Aguilera, Efredy, 2016. "Adaptive synchronization of fractional Lorenz systems using a reduced number of control signals and parameters," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 1-11.
    • Handle: RePEc:eee:chsofr:v:87:y:2016:i:c:p:1-11
    DOI: 10.1016/j.chaos.2016.02.038
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    References listed on IDEAS

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    1. Jian Yuan & Bao Shi & Wenqiang Ji, 2013. "Adaptive Sliding Mode Control of a Novel Class of Fractional Chaotic Systems," Advances in Mathematical Physics, Hindawi, vol. 2013, pages 1-13, September.
    2. Bernd Blasius & Amit Huppert & Lewi Stone, 1999. "Complex dynamics and phase synchronization in spatially extended ecological systems," Nature, Nature, vol. 399(6734), pages 354-359, May.
    3. Ping Zhou & Xiao-You Yang, 2011. "A Novel Hybrid Function Projective Synchronization between Different Fractional-Order Chaotic Systems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-15, August.
    4. Wang, Yan-Wu & Guan, Zhi-Hong, 2006. "Generalized synchronization of continuous chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 97-101.
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    Cited by:

    1. Wang, Cong & Zhang, Hong-li & Fan, Wen-hui, 2017. "Generalized dislocated lag function projective synchronization of fractional order chaotic systems with fully uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 14-21.
    2. Kocamaz, Uğur Erkin & Cevher, Barış & Uyaroğlu, Yılmaz, 2017. "Control and synchronization of chaos with sliding mode control based on cubic reaching rule," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 92-98.

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