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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

LIU Zhenguo1, SHI Yuyuan1, WU Yuqiang2   

  1. 1. School of Automation and Software Engineering, Shanxi University, Taiyuan 030006, China;
    2. Institute of Automation, Qufu Normal University, Qufu 273165, China
  • Received:2021-01-27 Revised:2021-05-03 Online:2022-10-25 Published:2022-10-12
  • Supported by:
    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.

LIU Zhenguo, SHI Yuyuan, WU Yuqiang. Tracking Control of Uncertain High-Order Nonlinear Systems with Odd Rational Powers and the Dead-Zone Input:A Direct Fuzzy Adaptive Control Method[J]. Journal of Systems Science and Complexity, 2022, 35(5): 1685-1699.

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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