Fundamental Trackability Problems for Iterative Learning Control

Generally, the classic iterative learning control (ILC) methods focus on finding design conditions for repetitive systems to achieve the perfect tracking of any specified trajectory, whereas they ignore a fundamental problem of ILC: whether the specified trajectory is trackable, or equivalently, whether there exist some inputs for the repetitive systems under consideration to generate the specified trajectory? The current paper contributes to dealing with this problem. Not only is a concept of trackability introduced formally for any specified trajectory in ILC, but also some related trackability criteria are established. Further, the relation between the trackability and the perfect tracking tasks for ILC is bridged, based on which a new convergence analysis approach is developed for ILC by leveraging properties of a functional Cauchy sequence (FCS). Simulation examples are given to verify the effectiveness of the presented trackability criteria and FCS-induced convergence analysis method for ILC.