Abstract
The goal of Iterative Learning Control (ILC) is to improve the accuracy of a system that repeatedly follows a reference trajectory. This paper proves that for any causal ILC, there is an equivalent feedback that achieves or approaches the ultimate ILC error with no iterations. Remarkably, this equivalent feedback depends only on the ILC operators and hence requires no plant knowledge. This equivalence is obtained whether or not the ILC includes current-cycle feedback. The equivalence is proved for general nonlinear systems, except for the special case of zero ultimate ILC error, which is investigated for LTI systems only. Conditions are obtained for internal stability and convergence of ILC, as these are used to prove equivalence in the zero error case. Since conventional feedback requires no iterations, there is no reason to use causal ILC.
Published Version
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