非线性系统的高阶迭代学习控制算法

Higher-Order Iterative Learning Control Algorithm for Nonlinear System

本文对一般非线性系统,提出了三种高阶迭代学习控制算法:(Ⅰ)u_(h+1)=sum from j=1 to r(P_ju_(k-j+1)+Г_je_(h-j+1));(Ⅱ)u_(k+1)=sum from j=1 to r(P_ju_(k-j+1)+F_je_(k-j+1));(Ⅲ)u_(k+1)=sum from j=1 to r{P_ju_(k-j+1)+(Г_j+F_jd/(dt))e_(k-j+1)},其中u_(k+1)=u_(k+1)(t)表示系统第k+1次运行时的输入;e_k=y_k-y_d;y_d是系统所期望的输出;y_k是系统第k次运行时的输出;P_j,Г_j,F_j(j=1,…,r)是常数阵;进而给出了比较弱的收敛性条件。

Three types of higher-order iterative learning control algorithm are presented for general nonlinear systems,which may be operated repeatedly at low cost. The convergency conditions are also obtained.