%0 Journal Article
%T Design of Iterative Learning Control Method with Global Convergence Property for Nonlinear Systems
%A Guang-Wei Xu
%A Cheng Shao
%A Yu Han
%J Journal of Control Science and Engineering
%D 2014
%I Hindawi Publishing Corporation
%R 10.1155/2014/351568
%X We address an iterative learning control (ILC) method for overcoming initial value problem caused by local convergence methods. Introducing a feedback recursive form of tracking errors into iterative learning law, this algorithm can avoid a crude linear approximation to nonlinear plants to reach global convergence property. The algorithmĄ¯s structure is entirely illustrated. Under assumptions, it is guaranteed that tracking errors of the closed-loop system converge to zero. Besides, we discuss the roles of parameters in iterative learning law for algorithm realization, and a nonlinear case study is presented to demonstrate the effectiveness and tracking performance of the proposed algorithm. 1. Introduction Iterative learning control (ILC) is a methodology for reducing errors from trial to trial for systems that operate repetitively. The objective of iterative learning control is to overcome the imperfect knowledge of system structure to improve tracking performance as few trials as possible. Since ILC issue is originally proposed by Arimoto et al. [1], applications of ILC can be widely found in industrial robot manipulator, chemical batch process, some medical equipment, manufacturing, and so forth [2¨C7]. The research of iterative learning control has been focusing on nonlinear systems. ILC algorithms based on optimization theory are effective methods to improve tracking performance of nonlinear systems. Xu and Tan [8] proposed Newton-type ILC scheme for nonlinear systems, and Du et al. [9] also provided Newton-type ILC scheme for known or identified continuous differential and monotonic system. Besides, Lin et al. [10] presented ILC algorithm based on Newton method for discrete nonlinear systems, and algorithm was implemented by decomposing nonlinear ILC problem into the sequence of linear time-varying ILC problems. Xu et al. [11] developed rank-one update to derive recurrent formula for approximating inverse matrix of Jacobian. Benefiting from usage of optimization theory, useful insights on performance improvement are presented in these articles. However, due to local or semilocal convergence properties, the difficult and important problem of finding an initial value close enough to the desired input so that error converges to zero remains. In fact, due to the unknown desired input in control process, it is rigorously hard to satisfy additional conditions of initial value. Therefore, convergence performance of methods mentioned above could have a greatly reduced quality. This paper develops an iterative learning control method with global convergence
%U http://www.hindawi.com/journals/jcse/2014/351568/