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非线性时变系统自适应backstepping学习控制
引用本文:赵瑾,唐东峰,郑海祥,孙云平,邹欣,王志强,吴笑峰.非线性时变系统自适应backstepping学习控制[J].数学的实践与认识,2009,39(10).
作者姓名:赵瑾  唐东峰  郑海祥  孙云平  邹欣  王志强  吴笑峰
作者单位:1. 湖南科技大学,信息与电气工程学院,湖南,湘潭,411201
2. 河北建筑工程学院,网络中心,河北,张家口,075024
摘    要:针对含有混合未知参数的高阶非线性系统,利用backstepping方法,提出了一种自适应重复学习控制方法,该方法与分段积分机制相结合,可以处理时变参数在一个未知紧集内周期性快时变的非线性系统,通过构造微分-差分参数自适应律,设计了一种自适应控制策略,使跟踪误差在误差平方范数意义下渐近收敛于零,利用Lyapunov泛函,给出了闭环系统收敛的一个充分条件.实例仿真结果说明了该方法的有效性.

关 键 词:混合型参数  backstepping  自适应控制  重复学习控制  Lyapunov泛函

Adaptive Backstepping Learning Control for a Class of Nonlinear Time-varying Systems
ZHAO Jin,TANG Dong-feng,ZHENG Hai-xiang,SUN Yun-ping,ZOU Xin,WANG Zhi-qiang,WU Xiao-feng.Adaptive Backstepping Learning Control for a Class of Nonlinear Time-varying Systems[J].Mathematics in Practice and Theory,2009,39(10).
Authors:ZHAO Jin  TANG Dong-feng  ZHENG Hai-xiang  SUN Yun-ping  ZOU Xin  WANG Zhi-qiang  WU Xiao-feng
Abstract:Combining the backstepping approach with the pointwise integral mechanism, a novel adaptive repetitive learning control for high-order nonlinear systems with time-varying and time-invariant parameters is proposed. It can be applied to the time-varying parametric uncertainty systems with unknown compact set, non-vanishing, rapid time-varying, periodic and where the prior knowledge is the periodicity only. A differential-difference adaptive law and an adaptive repetitive learning control one are constructed to ensure the asymptotic convergence of the tracking error in the sense of square error norm. Also, a sufficient condition of the convergence of the method is given. A simulation example illustrates the effectiveness of the proposed method.
Keywords:backstepping
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