Data informativity for tracking control of learning systems: Test and design conditions

How to develop control design methods directly based on the input and output data, instead of utilizing the system model, becomes a practically important topic in the control community. This paper explores the data informativity for the data-based control design methods, with a special focus on accomplishing the tracking objective for iterative learning control (ILC) systems. With the data collected under a certain test framework for ILC systems, a necessary and sufficient condition on the data informativity is provided for trackability of the desired reference, which is a premise for the realization of the perfect tracking objective. Based on the informative data for trackability, three classes of data-based ILC updating laws are designed to reach the perfect tracking objective for a group of ILC systems compatible with the informative data. Moreover, the data informativity for $\delta$-trackability of the desired reference is discussed with the focus on the more general $\delta$-tracking objective, under which a data-based ILC updating law is presented by only resorting to the informative data for $\delta$-trackability. In addition, for ILC systems with noises, the collected noisy data are leveraged to further exploit an ILC updating law to achieve the robust tracking objective. All the developed data-based ILC updating laws are applicable for any linear ILC system despite whether it is irregular or not, where the specific system model is not required.