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Adaptive chatter free sliding mode control for a class of uncertain chaotic systems

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  • Zhang, Xuxi
  • Liu, Xianping
  • Zhu, Qidan

Abstract

The chaos control for a class of uncertain chaotic system is studied. By using the Lyapunov stability theory and adaptive control technique, an adaptive chatter free sliding mode control is proposed without the knowledge of the bounds of the uncertain term representing the model uncertainty and unknown disturbance. Numerical simulation result is provided to show the effectiveness of the proposed control law.

Suggested Citation

  • Zhang, Xuxi & Liu, Xianping & Zhu, Qidan, 2014. "Adaptive chatter free sliding mode control for a class of uncertain chaotic systems," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 431-435.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:431-435
    DOI: 10.1016/j.amc.2014.01.094
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    References listed on IDEAS

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    1. Ge, Zheng-Ming & Yang, Cheng-Hsiung, 2009. "Chaos synchronization and chaotization of complex chaotic systems in series form by optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 994-1002.
    2. Yassen, M.T., 2006. "Chaos control of chaotic dynamical systems using backstepping design," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 537-548.
    3. El-Gohary, Awad & Yassen, Rizk, 2009. "Chaos and optimal control of a coupled dynamo with different time horizons," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 698-710.
    4. 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.
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    1. Shirkavand, Mehrdad & Pourgholi, Mahdi, 2018. "Robust fixed-time synchronization of fractional order chaotic using free chattering nonsingular adaptive fractional sliding mode controller design," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 135-147.
    2. Chen, Xiangyong & Park, Ju H. & Cao, Jinde & Qiu, Jianlong, 2017. "Sliding mode synchronization of multiple chaotic systems with uncertainties and disturbances," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 161-173.
    3. Liu, Zhen & Gao, Cunchen & Kao, Yonggui, 2015. "Robust H-infinity control for a class of neutral-type systems via sliding mode observer," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 669-681.
    4. Shirkavand, Mehrdad & Pourgholi, Mahdi & Yazdizadeh, Alireza, 2022. "Robust global fixed-time synchronization of different dimensions fractional-order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    5. Ijaz, Salman & Fuyang, Chen & Hamayun, Mirza Tariq & Anwaar, Haris, 2021. "Adaptive integral-sliding-mode control strategy for maneuvering control of F16 aircraft subject to aerodynamic uncertainty," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    6. Chen, Yuquan & Gao, Qing & Wei, Yiheng & Wang, Yong, 2017. "Study on fractional order gradient methods," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 310-321.
    7. Pai, Ming-Chang, 2015. "Discrete-time dynamic output feedback input shaping control of vibration in uncertain time-delay flexible structures," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 675-688.

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