Analysis of Transient Growth in Iterative Learning Control Using Pseudospectra

Douglas A. Bristow, Missouri University of Science and Technology
John R. Singler, Missouri University of Science and Technology

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In this paper we examine the problem of transient growth in Iterative Learning Co ntrol (ILC). Transient growth is generally avoided in design by using robust monotonic convergence (RMC) criteria. However, RMC leads to fundamental performance limitations. We consider the possibility of allowing safe transient growth in ILC algorithms as a means to circumvent these limitations. Here the pseudospectra is used for the first time to study transient growth in ILC. Basic properties of the pseudospectra that are relevant to the ILC problem are presented. Two ILC design problems are considered and examined using pseduospectra. The pseudospectra provides new results for these problems and illuminates the oft-misunderstood problem of transient growth.