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Control and synchronization of chaos with sliding mode control based on cubic reaching rule

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  • Kocamaz, Uğur Erkin
  • Cevher, Barış
  • Uyaroğlu, Yılmaz

Abstract

In this study, a new reaching rule in the Sliding Mode Control (SMC) is proposed for chaos control and synchronization. It is applied on the nonlinear Chua's circuit. The SMC signals are provided with the Lyapunov stability theory. Classical, cubic and partial cubic variants of SMC signals are constructed. Numerical simulations are performed to compare the effectiveness of the SMC signals and the results are discussed.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:105:y:2017:i:c:p:92-98
    DOI: 10.1016/j.chaos.2017.10.008
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    1. Zheng, Yongai & Ji, Zhilin, 2016. "Predictive control of fractional-order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 307-313.
    2. Sun, Mei & Jia, Qiang & Tian, Lixin, 2009. "A new four-dimensional energy resources system and its linear feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 101-108.
    3. Yan, Jun-Juh & Lin, Jui-Sheng & Liao, Teh-Lu, 2008. "Synchronization of a modified Chua’s circuit system via adaptive sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 45-52.
    4. Nazzal, Jamal M. & Natsheh, Ammar N., 2007. "Chaos control using sliding-mode theory," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 695-702.
    5. Haeri, Mohammad & Khademian, Behzad, 2006. "Comparison between different synchronization methods of identical chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 1002-1022.
    6. Peng, Chao-Chung & Chen, Chieh-Li, 2008. "Robust chaotic control of Lorenz system by backstepping design," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 598-608.
    7. 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.
    8. Agrawal, S.K. & Srivastava, M. & Das, S., 2012. "Synchronization of fractional order chaotic systems using active control method," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 737-752.
    9. Sun, Jitao & Zhang, Yinping, 2004. "Impulsive control and synchronization of Chua’s oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(6), pages 499-508.
    10. Ghamati, Mina & Balochian, Saeed, 2015. "Design of adaptive sliding mode control for synchronization Genesio–Tesi chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 111-117.
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