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Adaptive Neural Tracking Control for Nonstrict-Feedback Nonlinear Systems with Unknown Control Gains via Dynamic Surface Control Method

Author

Listed:
  • Xiongfeng Deng

    (Key Laboratory of Advanced Perception and Intelligent Control of High-End Equipment, Ministry of Education, Anhui Polytechnic University, Wuhu 241000, China
    Key Laboratory of Electric Drive and Control of Anhui Higher Education Institutes, Anhui Polytechnic University, Wuhu 241000, China)

  • Yiming Yuan

    (Key Laboratory of Advanced Perception and Intelligent Control of High-End Equipment, Ministry of Education, Anhui Polytechnic University, Wuhu 241000, China)

  • Lisheng Wei

    (Key Laboratory of Advanced Perception and Intelligent Control of High-End Equipment, Ministry of Education, Anhui Polytechnic University, Wuhu 241000, China)

  • Binzi Xu

    (Key Laboratory of Advanced Perception and Intelligent Control of High-End Equipment, Ministry of Education, Anhui Polytechnic University, Wuhu 241000, China)

  • Liang Tao

    (Key Laboratory of Advanced Perception and Intelligent Control of High-End Equipment, Ministry of Education, Anhui Polytechnic University, Wuhu 241000, China)

Abstract

This paper addresses the tracking control problem of nonstrict-feedback systems with unknown control gains. The dynamic surface control method, Nussbaum gain function control technique, and radial basis function neural network are applied for the design of virtual control laws, and adaptive control laws. Then, an adaptive neural tracking control law is proposed in the last step. By using the dynamic surface control method, the “explosion of complexity” problem of conventional backstepping is avoided. Based on the application of the Nussbaum gain function control technique, the unknown control gain problem is well solved. With the help of the radial basis function neural network, the unknown nonlinear dynamics are approximated. Furthermore, through Lyapunov stability analysis, it is proved that the proposed control law can guarantee that all signals in the closed-loop system are bounded and the tracking error can converge to an arbitrarily small domain of zero by adjusting the design parameters. Finally, two examples are provided to illustrate the effectiveness of the proposed control law.

Suggested Citation

  • Xiongfeng Deng & Yiming Yuan & Lisheng Wei & Binzi Xu & Liang Tao, 2022. "Adaptive Neural Tracking Control for Nonstrict-Feedback Nonlinear Systems with Unknown Control Gains via Dynamic Surface Control Method," Mathematics, MDPI, vol. 10(14), pages 1-13, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2419-:d:860228
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    References listed on IDEAS

    as
    1. Yongchao Liu & Qidan Zhu, 2021. "Adaptive fuzzy event-triggered control for nonstrict-feedback switched stochastic nonlinear systems with state constraints," International Journal of Systems Science, Taylor & Francis Journals, vol. 52(14), pages 2889-2903, October.
    2. Xiongfeng Deng & Jiakai Wang, 2022. "Fuzzy-Based Adaptive Dynamic Surface Control for a Type of Uncertain Nonlinear System with Unknown Actuator Faults," Mathematics, MDPI, vol. 10(10), pages 1-21, May.
    3. Ma, Qian, 2017. "Cooperative control of multi-agent systems with unknown control directions," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 240-252.
    4. Yang, Wei & Cui, Guozeng & Ma, Qian & Ma, Jiali & Tao, Chongben, 2022. "Finite-time adaptive event-triggered command filtered backstepping control for a QUAV," Applied Mathematics and Computation, Elsevier, vol. 423(C).
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