基于向量图分析的迭代学习控制非线性算法

Iterative learning control nonlinear algorithms based on vector plots analysis

打破多年来人们一直囿于Arimoto的思路 ,另辟途径寻找新的迭代学习控制的研究方法 ,以期构架迭代学习控制的几何理论 .基于数学的几何方法 ,通过对通常算法所构成的向量图进行分析 ,获得了一类快速的迭代学习控制新算法 ,然后对这种新结构的算法在理论上进行了完整的收敛性分析 .这类新算法与目前所有迭代学习控制算法不同 ,具有非线性结构 .

A new approach to seek the research method of the iterative learning control is proposed,which is completely different from Arimoto's idea.The purpose of the attempt is to establish the geometrical theory of iterative learning control.Based on the mathematical geometrical analysis,this paper obtains a class of new fast algorithms of iterative learning control by analyzing the vector plots of the basic algorithms.Then,for the new structure of algorithms,a complete theoretical analysis of convergence is given.The new algorithm is different from the algorithms of iterative learning control proposed recently,and is with nonlinear structure.Simulations illustrate the effectiveness and superiority of the new algorithms.