STABILITY, CONVERGENCE, AND FEEDBACK EQUIVALENCE OF LTI ITERATIVE LEARNING CONTROL
Peter B. Goldsmith
Department of Mechanical and Manufacturing Engineering, University of Calgary, Canada T2N 1N4
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.
Keywords: Iterative learning control; Feedback control; Stability; Convergence; Linear systems
Session slot T-Th-A03: Iterative Control Design/Area code 3b : Adaptive Control and Tuning

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