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Adaptive sliding mode control of chaotic dynamical systems with application to synchronization

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  • Dadras, Sara
  • Momeni, Hamid Reza

Abstract

We address the problem of control and synchronization of a class of uncertain chaotic systems. Our approach follows techniques of sliding mode control and adaptive estimation law. The adaptive algorithm is constructed based on the sliding mode control to ensure perfect tracking and synchronization in presence of system uncertainty and external disturbance. Stability of the closed-loop system is proved using Lyapunov stability theory. Our theoretical findings are supported by simulation results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:80:y:2010:i:12:p:2245-2257
    DOI: 10.1016/j.matcom.2010.04.005
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    References listed on IDEAS

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    1. Park, Ju H., 2006. "Chaos synchronization between two different chaotic dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 549-554.
    2. Chang, Wei-Der & Yan, Jun-Juh, 2005. "Adaptive robust PID controller design based on a sliding mode for uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 167-175.
    3. Li, Wang-Long & Chang, Kuo-Ming, 2009. "Robust synchronization of drive–response chaotic systems via adaptive sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2086-2092.
    4. Sun, Huijing & Cao, Hongjun, 2008. "Chaos control and synchronization of a modified chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1442-1455.
    5. Zhang, Qunjiao & Lu, Jun-an, 2008. "Chaos synchronization of a new chaotic system via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 175-179.
    6. Dadras, Sara & Momeni, Hamid Reza, 2009. "Control uncertain Genesio–Tesi chaotic system: Adaptive sliding mode approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3140-3146.
    7. Dadras, Sara & Momeni, Hamid Reza & Majd, Vahid Johari, 2009. "Sliding mode control for uncertain new chaotic dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1857-1862.
    8. Salarieh, Hassan & Shahrokhi, Mohammad, 2008. "Adaptive synchronization of two different chaotic systems with time varying unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 125-136.
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    Cited by:

    1. 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.
    2. 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.
    3. Hamida, Mohamed Assaad & Glumineau, Alain & de Leon, Jesus & Loron, Luc, 2014. "Robust adaptive high order sliding-mode optimum controller for sensorless interior permanent magnet synchronous motors," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 105(C), pages 79-104.
    4. Heydari, Mahdi & Salarieh, Hassan & Behzad, Mehdi, 2011. "Stochastic chaos synchronization using Unscented Kalman–Bucy Filter and sliding mode control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(9), pages 1770-1784.
    5. 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.

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