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Generalized adaptive backstepping sliding mode control for synchronizing chaotic systems with uncertainties and disturbances

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  • Pal, Pikaso
  • Mukherjee, V.
  • Alemayehu, Hinsermu
  • Jin, Gang Gyoo
  • Feyisa, Gosa

Abstract

This article focuses on the synchronization problem of different chaotic systems where both the systems (i.e., master and slave) are anticipated to be perturbed with external disturbances and model uncertainties. The control problem of synchronization is addressed with a robust aggregate of backstepping with sliding mode control provided the bound of uncertainty is known and available. However, obtaining the bound of uncertainties in practical applications is considerably difficult. An adaptation law is used to estimate the uncertainty. The proposed control scheme practices the Lyapunov stability theory to confirm the asymptotic stability of the closed-loop system. Subsequently, a set of simulation works in detail are presented to validate the effectiveness of the chaos synchronization method.

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  • Pal, Pikaso & Mukherjee, V. & Alemayehu, Hinsermu & Jin, Gang Gyoo & Feyisa, Gosa, 2021. "Generalized adaptive backstepping sliding mode control for synchronizing chaotic systems with uncertainties and disturbances," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 793-807.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:793-807
    DOI: 10.1016/j.matcom.2021.06.018
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    References listed on IDEAS

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    1. Farivar, Faezeh & Shoorehdeli, Mahdi Aliyari & Nekoui, Mohammad Ali & Teshnehlab, Mohammad, 2009. "Generalized projective synchronization for chaotic systems via Gaussian Radial Basis Adaptive Backstepping Control," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 826-839.
    2. Park, Ju H., 2009. "A note on synchronization between two different chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1538-1544.
    3. Handa, Himesh & Sharma, B.B., 2016. "Novel adaptive feedback synchronization scheme for a class of chaotic systems with and without parametric uncertainty," Chaos, Solitons & Fractals, Elsevier, vol. 86(C), pages 50-63.
    4. Park, Ju H., 2006. "Synchronization of a class of chaotic dynamic systems with controller gain variations," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1279-1284.
    5. Lei, Youming & Xu, Wei & Shen, Jianwei & Fang, Tong, 2006. "Global synchronization of two parametrically excited systems using active control," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 428-436.
    6. Chen, Hsien-Keng, 2005. "Global chaos synchronization of new chaotic systems via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1245-1251.
    7. Yu, Yongguang, 2008. "Adaptive synchronization of a unified chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 329-333.
    8. M. M. El-Dessoky & M. T. Yassen, 2012. "Adaptive Feedback Control for Chaos Control and Synchronization for New Chaotic Dynamical System," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-12, June.
    9. Dadras, Sara & Momeni, Hamid Reza, 2010. "Adaptive sliding mode control of chaotic dynamical systems with application to synchronization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(12), pages 2245-2257.
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    Cited by:

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