非线性时变系统自适应backstepping学习控制  

Adaptive Backstepping Learning Control for a Class of Nonlinear Time-varying Systems

作　　者：赵瑾[1] 唐东峰[1] 郑海祥[1] 孙云平[1] 邹欣[2] 王志强[1] 吴笑峰[1] 

机构地区：[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

出　　处：《数学的实践与认识》2009年第10期232-238,共7页Mathematics in Practice and Theory

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.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.

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

分 类 号：O231[理学—运筹学与控制论]