Fundamental Trackability Problems for Iterative Learning Control

TL;DR

This paper introduces the concept of trackability in iterative learning control (ILC), establishing criteria to determine if a trajectory can be achieved, and develops a new convergence analysis approach based on functional Cauchy sequences.

Contribution

It formally defines trackability in ILC, provides criteria for it, and links it to convergence analysis, advancing understanding of trajectory feasibility in repetitive control systems.

Findings

Proposed formal concept of trackability for ILC trajectories

Established criteria to assess trajectory trackability

Developed a convergence analysis method using functional Cauchy sequences

Abstract

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.