Analysis of Linear Iterative Learning Control Schemes - A 2D Systems/Repetitive Processes Approach

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.