High-order iterative learning controller with initial state learning

A common assumption in iterative learning control (ILC) is that the initial states in each repetitive operation should be inside a given ball centred at the desired initial states. This assumption is critical to the stability analysis, and the size of the ball will directly affect the 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 learning scheme together with a high-order D-type ILC updating law. Nonlinear time-dependent uncertain systems are investigated. Uniform bounds of the tracking errors are obtained. These bounds depend only on the bounds of the differences of the uncertainties and disturbances between two successive system repetitions, and not on the re-initialization errors. The unknown desired initial states can be identified through learning iterations. Furthermore, better learning transient behaviour can be expected as the iteration number increases, by using the high-order scheme. This result is illustrated by simulations.