A high-order iterative learning controller with initial state learning

Abstract

A common assumption in iterative learning control (ILC) is that the initial states in eachrepetitive operation should be inside a given ball centred at the desired initial states. Thisassumption is critical to the stability analysis, and the size of the ball will directly affectthe final output-trajectory tracking errors. However, the initial state may be unobtainable.In this paper, the assumption can be removed by using a high-order initial-state learningscheme together with a high-order D-type ILC updating law. Nonlinear time-dependentuncertain systems are investigated. Uniform bounds of the tracking errors are obtained.These bounds depend only on the bounds of the differences of the uncertainties anddisturbances between two successive system repetitions, and not on the re-initializationerrors. The unknown desired initial states can be identified through learning iterations.Furthermore, better learning transient behaviour can be expected as the iteration numberincreases, by using the high-order scheme. This result is illustrated by simulations.Keywords: Learning control; repetitive systems; nonlinear systems; uncertainty; trackingcontrol; re-initialization error.