Set-to-set iterative learning control

For some iterative learning control (ILC) applications, obtaining sets or regions at specific times is desired rather than tracking a specific reference at these times. Within these sets or regions, no reference is provided for tracking, so either reference-free tracking of the sets must be done or a reference must be created within the sets. While existing approaches such as region-to-region ILC create a reference within the sets, this paper extends the ILC literature by developing a novel set-to-set (STS) ILC which performs reference-free tracking of the time-indexed sets. Analysis of the STS ILC demonstrates that by tracking the sets in a reference-free manner, the optimization cost of the STS ILC will lower bound that of alternative ILC methods. Additionally, despite an unknown repetitive disturbance, the STS ILC update law causes the output trajectory to lie within the sets at all desired times. Two case studies are used to demonstrate the effectiveness of the approach in allowing a linear system agent to visit polytopic set regions by learning the correct paths from one iteration to the next.