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Tracking Control of Uncertain High-Order Nonlinear Systems with Odd Rational Powers and the Dead-Zone Input: A Direct Fuzzy Adaptive Control Method

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Abstract

This work studies the tracking issue of uncertain nonlinear systems. The existence of odd rational powers, multiple unknown parameters and the dead-zone input add many difficulties for control design. During procedures of the control design, by introducing an appropriate Lyapunov function, utilizing recursive control method and the inequality technique, some appropriate intermediate auxiliary control laws are designed under the hypothesis that nonlinear terms in the system are known. When those nonlinear terms are unknown, by employing the powerful approximation ability of fuzzy systems, the intermediate auxiliary control laws are approximated recursively and used to construct the virtual control. Finally, a new fuzzy adaptive tracking controller is constructed to ensure a small tracking error and the boundedness of all states. In this paper, the overparameterization problem is significantly avoided since only two adaptive laws are adopted. Numerical and practical examples are used to verify the raised theory.

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Author information

Authors and Affiliations

  1. School of Automation and Software Engineering, Shanxi University, Taiyuan, 030006, China

    Zhenguo Liu & Yuyuan Shi

  2. Institute of Automation, Qufu Normal University, Qufu, 273165, China

    Yuqiang Wu

Authors
  1. Zhenguo Liu
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  2. Yuyuan Shi
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  3. Yuqiang Wu
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Corresponding author

Correspondence to Zhenguo Liu.

Additional information

This paper was supported by Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (STIP) under Grant No. 2019L0011, and the Major Scientific and Technological Innovation Project in Shandong Province under Grant No. 2019JZZY011111.

This paper was recommended for publication by Editor YU Jinpeng.

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Liu, Z., Shi, Y. & Wu, Y. Tracking Control of Uncertain High-Order Nonlinear Systems with Odd Rational Powers and the Dead-Zone Input: A Direct Fuzzy Adaptive Control Method. J Syst Sci Complex 35, 1685–1699 (2022). https://doi.org/10.1007/s11424-022-1011-1

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  • DOI: https://doi.org/10.1007/s11424-022-1011-1

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