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Adaptive fuzzy tracking control for stochastic nonlinear systems with unknown time-varying delays

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  • Li, Junmin
  • Yue, Hongyun

Abstract

This paper addresses the problem of adaptive tracking control for a class of stochastic strict-feedback nonlinear time-varying delays systems using fuzzy logic systems (FLS). In this paper, quadratic functions are used as Lyapunov functions to analyze the stability of systems, other than the fourth moment approach proposed by H. Deng and M. Krstic, and the hyperbolic tangent functions are introduced to deal with the Hessian terms. This approach overcomes the drawback of the traditional quadratic moment approach and reduce the complexity of design procedure and controller. Based on the backstepping technique, the appropriate Lyapunov–Krasovskii functionals and the FLS, the adaptive fuzzy controller is well designed. The proposed adaptive fuzzy controller guarantees that all the signals in the closed-loop system are bounded in probability and the tracking error can converge to a small residual set around the origin in the mean square sense.

Suggested Citation

  • Li, Junmin & Yue, Hongyun, 2015. "Adaptive fuzzy tracking control for stochastic nonlinear systems with unknown time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 514-528.
    • Handle: RePEc:eee:apmaco:v:256:y:2015:i:c:p:514-528
    DOI: 10.1016/j.amc.2014.12.104
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    Cited by:

    1. Liu, Yanli & Wang, Runzhi & Hao, Li-Ying, 2022. "Adaptive TD control of full-state-constrained nonlinear stochastic switched systems," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    2. Xin, Li-Ping & Yu, Bo & Zhao, Lin & Yu, Jinpeng, 2020. "Adaptive fuzzy backstepping control for a two continuous stirred tank reactors process based on dynamic surface control approach," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    3. Xi, Changjiang & Dong, Jiuxiang, 2019. "Adaptive fuzzy guaranteed performance control for uncertain nonlinear systems with event-triggered input," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    4. Min, Huifang & Xu, Shengyuan & Yu, Xin & Fei, Shumin & Cui, Guozeng, 2020. "Adaptive Tracking Control for Stochastic Nonlinear Systems with Full-State Constraints and Unknown Covariance Noise," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    5. Zhai, Ding & Lu, An-Yang & Dong, Jiuxiang & Zhang, Qing-Ling, 2017. "Stability analysis and state feedback control of continuous-time T–S fuzzy systems via anew switched fuzzy Lyapunov function approach," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 586-599.
    6. Heng Liu & Ye Chen & Guanjun Li & Wei Xiang & Guangkui Xu, 2017. "Adaptive Fuzzy Synchronization of Fractional-Order Chaotic (Hyperchaotic) Systems with Input Saturation and Unknown Parameters," Complexity, Hindawi, vol. 2017, pages 1-16, November.
    7. Wang, Yingchun & Zhang, Jiaxin & Zhang, Huaguang & Xie, Xiangpeng, 2021. "Finite-time adaptive neural control for nonstrict-feedback stochastic nonlinear systems with input delay and output constraints," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    8. Xiao, Wenbin & Cao, Liang & Dong, Guowei & Zhou, Qi, 2019. "Adaptive fuzzy control for pure-feedback systems with full state constraints and unknown nonlinear dead zone," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 354-371.
    9. Dong, Jiuxiang & Hou, Junteng, 2017. "Output feedback fault-tolerant control by a set-theoretic description of T–S fuzzy systems," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 117-134.

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