Linear and nonlinear iterative learning control
type: Item
instance of: scholarly article
title: Linear and nonlinear iterative learning control
zbMATH Open document ID: 1021.93002
DOI: 10.1007/3-540-44845-4
author: Jian-Xin Xu
author: Ying Tan
published in: Lecture Notes in Control and Information Sciences
publication date: 2003-07-22T00:00:00Z
review text: ``Iterative Learning Control'' (ILC) is a design technique which was first divised by S. Arimoto and colleagues about twenty years ago. The goal is to track exactly a given trajectory with suitable controls. The setting is that an experiment is repeated after a given interval of time has elapsed. There is a law which gives the value of the new control from the preceding one (depending on the error of the tracked profiles). This is where learning occurs. The initial conditions are always the same at the start of each iteration, but the control construction depends a priori on it so that it is not allowed to speak of feedback without detailed analysis. After an introductory section (idea of the method, history of the discipline, outline of the book), the situation using a contraction mapping theorem is presented. A global Lipschitz condition on the plant is assumed. The authors explore issues of convergence and try to determine if memory of more than one iteration is needed. The MIMO and nonlinear cases are studied in succession. A second part considers the more general situation of a local Lipschitz condition as an hypothesis on the plant. A ``composite energy function'' is used. The idea is to decompose the control into a stabilizing feedback and a learning control. The authors make connections with optimal control theory and a last chapter uses wavelets in this context. A conclusion points out open areas of research: further study of convergence issues when using the ``composite energy function'' method (which performs worse than the contraction mapping method), the discrete case, observation problems, analytic solutions, and the use of other learning methods (normal nets, statistical learning, etc.\dots). There are 153 references and an index. A chapter relating ILC and 2-D systems theory would have been welcome. The book will be of interest for teaching and learning ``iterative learning control''.
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93B51
Mathematics Subject Classification ID: 68T05
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93C35
zbMATH DE Number: 1952028
zbMATH Keywords: tracking
zbMATH Keywords: nonlinear system
zbMATH Keywords: MIMO system
zbMATH Keywords: iterative learning control
zbMATH Keywords: composite energy function
zbMATH Keywords: design
zbMATH Keywords: contraction mapping theorem
zbMATH Keywords: global Lipschitz condition
zbMATH Keywords: convergence
zbMATH Keywords: memory
zbMATH Keywords: local Lipschitz condition
zbMATH Keywords: optimal control
zbMATH Keywords: wavelets
reviewed by: A. Akutowicz
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/3-540-44845-4
OpenAlex ID: W614117236
description: scientific article; zbMATH DE number 1952028