Multidimensional Systems and Signal Processing
, Volume 11, Issue 1, pp 125177
First online:
Analysis of Linear Iterative Learning Control Schemes  A 2D Systems/Repetitive Processes Approach
 D. H. OwensAffiliated withDepartment of Automatic Control and Systems Engineering, University of Sheffield
 , N. AmannAffiliated with
 , E. RogersAffiliated withDepartment of Electronics and Computer Science, University of Southampton
 , M. FrenchAffiliated withDepartment of Electronics and Computer Science, University of Southampton
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This paper first develops results on the stability and convergence properties of a general class of iterative learning control schemes using, in the main, theory first developed for the branch of 2D linear systems known as linear repetitive processes. A general learning law that uses information from the current and a finite number of previous trials is considered and the results, in the form of fundamental limitations on the benefits of using this law, are interpreted in terms of basic systems theoretic concepts such as the relative degree and minimum phase characteristics of the example under consideration. Following this, previously reported powerful 2D predictive and adaptive control algorithms are reviewed. Finally, new iterative adaptive learning control laws which solve iterative learning control algorithms under weak assumptions are developed.
 Title
 Analysis of Linear Iterative Learning Control Schemes  A 2D Systems/Repetitive Processes Approach
 Journal

Multidimensional Systems and Signal Processing
Volume 11, Issue 12 , pp 125177
 Cover Date
 200004
 DOI
 10.1023/A:1008494815252
 Print ISSN
 09236082
 Online ISSN
 15730824
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 repetitive processes
 iterative learning
 adaptive control
 Industry Sectors
 Authors

 D. H. Owens ^{(1)}
 N. Amann ^{(2)}
 E. Rogers ^{(3)}
 M. French ^{(3)}
 Author Affiliations

 1. Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK
 2. Daimlerchrysler, Berlin, Germany
 3. Department of Electronics and Computer Science, University of Southampton, Southampton, SO17 1BJ, UK