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Adaptive Control Design for Arneodo Chaotic System with Uncertain Parameters and Input Saturation

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  • Chunhua Cheng
  • Fengjuan Gao
  • Jingshuo Xu
  • Yuanxin Wang
  • Tao Yuan

Abstract

In this paper, tracking controller and synchronization controller of the Arneodo chaotic system with uncertain parameters and input saturation are considered. An adaptive tracking control law and an adaptive synchronization control law are proposed based on backstepping and Lyapunov stability theory. The adaptive laws of the unknown parameters are derived by using the Lyapunov stability theory. To handle the effect caused by the input saturation, an auxiliary system is used to compensate the tracking error and synchronization error. The proposed adaptive tracking control and synchronization schemes ensure the effects of tracking and synchronization. Several examples have been detailed to illuminate the design procedure.

Suggested Citation

  • Chunhua Cheng & Fengjuan Gao & Jingshuo Xu & Yuanxin Wang & Tao Yuan, 2020. "Adaptive Control Design for Arneodo Chaotic System with Uncertain Parameters and Input Saturation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:3285414
    DOI: 10.1155/2020/3285414
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    References listed on IDEAS

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    1. Mou, Chen & Jiang, Chang-sheng & Bin, Jiang & Wu, Qing-xian, 2009. "Sliding mode synchronization controller design with neural network for uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1856-1863.
    2. Li, Xian-Feng & Chu, Yan-Dong & Leung, Andrew Y.T. & Zhang, Hui, 2017. "Synchronization of uncertain chaotic systems via complete-adaptive-impulsive controls," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 24-30.
    3. Kim, Jae-Hun & Park, Chang-Woo & Kim, Euntai & Park, Mignon, 2005. "Adaptive synchronization of T–S fuzzy chaotic systems with unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1353-1361.
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