Stabilizability, performance, and the choice of actuation and observation time windows in Iterative Learning Control

In this paper, we analyze the trial domain stabilizability of iterative learning control (ILC) for linear time varying systems. We prove that a system can only be made asymptotically stable in trial domain if the number of trial domain integrators does not exceed the rank of the convolutive i/o system map. Based on this statement, a general ILC control structure is formulated in which asymptotic stability and optimal performance can be obtained by separate components in the controller. Furthermore, we prove that systems with certain properties have the additional freedom to manipulate the signal form of the command signal. Subsequently, we introduce an actuation and observation time window in the ILC controlled system, making it possible to capture nonstandard ILC problems within a single general framework. The effect of these time windows on the ILC controlled system and the design freedom of the ILC controller is discussed, and illustrated by five applications