您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (7): 134-144.doi: 10.6040/j.issn.1671-9352.0.2024.428

• • 上一篇    

基于时变幂和参数不确定性的非线性系统自适应有限时间控制

赵冉,蒋蒙蒙*,牛霄   

  1. 聊城大学数学科学学院, 山东 聊城 252059
  • 发布日期:2026-07-01
  • 通讯作者: 蒋蒙蒙(1989— ),女,讲师,博士,研究方向为非线性系统控制. E-mail:jmm725@163.com
  • 作者简介:赵冉(2002— ),女,硕士研究生,研究方向为非线性系统控制. E-mail:zr021219@163.com*通信作者:蒋蒙蒙(1989— ),女,讲师,博士,研究方向为非线性系统控制. E-mail:jmm725@163.com
  • 基金资助:
    国家自然科学基金青年项目(62103175)

Adaptive finite-time control of nonlinear systems based on time-varying powers and parametric uncertainties

ZHAO Ran, JIANG Mengmeng*, NIU Xiao   

  1. School of Mathematics Science, Liaocheng University, Liaocheng 252059, Shandong, China
  • Published:2026-07-01

PDF (PC)

3

摘要： 本文研究具有参数不确定性的非线性系统中的自适应有限时间控制问题。该类系统的阶次不是常数而是时变函数且非线性函数中含有参数不确定性。结合Lyapunov函数、符号函数、添加幂积分器与自适应控制方法,设计自适应状态反馈控制器。该控制器能够在系统参数不确定且系统阶次为时变函数时,确保系统是半全局实用有限时间稳定的。最后,仿真结果验证所提出的控制方法的可行性和有效性。

关键词: 参数不确定性, 非线性系统, 半全局实用有限时间稳定, 自适应控制

Abstract: For a class of nonlinear systems with parameter uncertainty, the adaptive finite time control problem is studied. The powers of the system are time-varying functions instead of constants, and the nonlinear functions contain parametric uncertainties. In order to solve this problem, an adaptive state feedback controller is designed by cleverly combining the Lyapunov function, the symbolic function, adding a power integrator and adaptive control method, which can ensure that the system with parameter uncertainties and time-varying powers is semi-global practical finite time stability. Finally, the simulation results verify the feasibility and effectiveness of the control method proposed in this study.

Key words: parametric uncertainties, nonlinear systems, semi-globally practical finite-time stable, adaptive control

中图分类号: 

  • O231
[1] 陈海,郭肖旺,刘琛,等. 基于干扰观测器的复杂非线性系统优化控制方法[J]. 东南大学学报(自然科学版),2024,54(4):1046-1052. Chen Hai, Guo Xiaowang, Liu Chen, et al. Optimal control method for complex nonlinear systems based on disturbance observer[J]. Journal of Southeast University(Natural Science Edition), 2024, 54(4):1046-1052.
[2] Zhang W G, Yan J. Adaptive constrained output feedback optimal consensus tracking for uncertain nonlinear multi-agent systems and its application[J]. International Journal of Control, 2024, 97(3):600-614.
[3] Zhao S W, Wang J C, Wang H Y, et al. Goal representation adaptive critic design for discrete-time uncertain systems subjected to input constraints:the event-triggered case[J]. Neurocomputing, 2022, 492:676-688.
[4] Liu Y A, Xia J W, Wang J, et al. Finite-time stability for interval type-2 fuzzy nonlinear systemsvia an observer-based sliding mode control[J]. Journal of Systems Science and Complexity, 2022, 35(6):2223-2247.
[5] Wang Y D, Zong G D, Yang D, et al. Finite-time adaptive tracking control for a class ofnonstrict feedback nonlinear systems with full state constraints[J]. International Journal of Robust and Nonlinear Control, 2022, 32(5):2551-2569.
[6] Gao R, Huang J S, Su X J, et al. K-filter-based adaptive output feedback control for high-order nonlinear systems subject to actuator and sensor attacks[J]. International Journal of Robust and Nonlinear Control, 2022, 32(6):3469-3484.
[7] Bataghva M, Hashemi M. Adaptive sliding modesynchronisation for fractional-order non-linear systems in the presence of time-varying actuator faults[J]. IET Control Theory & Applications, 2022, 16(9):916-924.
[8] Niu B, Liu M, Li A. Global adaptive stabilization of stochastic high-order switched nonlinear non-lower triangular systems[J]. Systems & Control Letters, 2020, 136:104596.
[9] Wang N, Fu Z M, Tao F Z, et al. Adaptive fuzzy fixed-time control for a class of strict-feedback stochastic nonlinear systems[J]. Systems Science & Control Engineering, 2022, 10(1):142-153.
[10] Song Z B, Zhai J Y. Decentralized output feedback stabilization for switched stochastic high-order nonlinear systems with time-varying state/input delays[J]. ISA Transactions, 2019, 90:64-73.
[11] Liu Z G, Sun W, Zhang W D. Robust adaptive control for uncertain nonlinear systems with odd rational powers, unmodeled dynamics, and non-triangular structure[J]. ISA Transactions, 2022, 128:81-89.
[12] Hashemi M, Askari J, Ghaisari J, et al. Robust adaptive actuator failure compensation for a class of uncertain nonlinear systems[J]. International Journal of Automation and Computing, 2017, 14(6):719-728.
[13] Yan C H, Zhang W, Li X H, et al. Observer-based time-varying formation tracking for one-sidedLipschitz nonlinear systems via adaptive protocol[J]. International Journal of Control, Automation and Systems, 2020, 18(11):2753-2764.
[14] Rodrigo Marco V, Kalkkuhl J C, Raisch J, et al. Regularized adaptive Kalman filter for non-persistently excited systems[J]. Automatica, 2022, 138:110147.
[15] Shao Y, Xu S Y, Li Y M, et al. Globalstabilisation for a class of stochastic continuous non-linear systems with time-varying delay[J]. IET Control Theory & Applications, 2021, 15(2):297-306.
[16] Liu Y, Liu X P, Jing Y W, et al. Semi-globally practical finite-time stability for uncertain nonlinear systems based on dynamic surface control[J]. International Journal of Control, 2021, 94(2):476-485.
[17] Jiang M M, Zhang K M, Xie X J. Adaptive finite-time control of uncertain nonlinear systems with the powers of odd rational numbers[J]. International Journal of Systems Science, 2018, 49(14):2912-2922.
[18] Jiang M M, Xie X J. Adaptive finite-time stabilization of high-order nonlinear systems with dynamic and parametric uncertainties[J]. Mathematical Problems in Engineering, 2016, 2016:5702182.
[19] Yuan M M. Event-triggered adaptive control for stochastic p-normal switched feedforward systems with time-varying delays[J]. Circuits, Systems, and Signal Processing, 2023, 42(4):2065-2087.
[20] Sun Z Y, Shao Y, Chen C C. Fast finite-time stability and its application in adaptive control of high-order nonlinear system[J]. Automatica, 2019, 106:339-348.
[21] Dong S J, Li Y M. Adaptive fuzzy finite-time formation asymptotic tracking control for nonholonomic multirobot systems with inputs quantization[J]. International Journal of Adaptive Control and Signal Processing, 2023, 37(11):2875-2894.
[1] 杨叶红,肖剑*,马珍珍. 一个新分数阶混沌系统的同步和控制[J]. 山东大学学报（理学版）, 2014, 49(2): 76-83.
[2] 李双宝. 一类6维非线性系统的多脉冲同宿轨道的研究[J]. J4, 2012, 47(7): 100-105.
[3] 刘万海,沈艳军*,任欣军. 一类单输入单输出非线性系统全局有限时间输出反馈控制[J]. J4, 2012, 47(7): 106-116.
[4] . 一类非线性系统有限时间稳定控制的新方法[J]. J4, 2009, 44(7): 55-61.
[5] 孙炜伟,王玉振 . 几类时滞非线性哈密顿系统的稳定性分析[J]. J4, 2007, 42(12): 1-09 .
[6] 张 卫,鞠培军 . 含未知输入的Lipschitz非线性广义系统的观测器设计[J]. J4, 2006, 41(2): 85-88 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发