任意初值非线性不确定系统的迭代学习控制

摘要

为解决任意初态下的轨迹跟踪问题，针对一类含参数和非参数不确定性的非线性系统，提出基于滤波误差初始修正的自适应迭代学习控制方法。利用修正滤波误差信号设计学习控制器，并以Lyapunov 方法进行收敛性能分析。依据类Lipschitz条件处理非参数不确定性，对于处理过程中出现的未知时变参数向量，利用自适应迭代学习机制进行估计。经过足够多次迭代后，藉由修正滤波误差在整个作业区间收敛于零，实现滤波误差本身在预设的作业区间也收敛于零。仿真结果表明了本文所提控制方法的有效性。%This paper presents a filtering-error rectified adaptive iterative learning control method to tackle the trajectory-tracking problem for a class of both parametric and nonparametric uncertain systems in the presence of arbi-trary initial states. A novel rectification is made to modify the filtering-error error signal such that the learning control design and performance analysis could be simplified and easy for implementation. The proposed learning control design is a Lyapunov synthesis-based adaptive iterative learning control scheme. The Lipschitz-like assumption is used for handling nonparametric uncertainties, where the estimation for unknown time-varying parameters is given by learning mechanisms. As iteration increases, the rectified filtering-error converges to zero over the entire time interval, and the filtering-error itself converges to zero on the specified interval. Numerical results are presented to demonstrate effectiveness of the proposed learning control scheme.