Robust Monotonic Convergent Iterative Learning Control Design: an LMI-based Method

TL;DR

This paper presents an LMI-based method for designing robust, monotonic convergent iterative learning control algorithms that optimize convergence speed for uncertain linear systems, with flexible learning function order.

Contribution

It introduces a new LMI-based approach using SOS conditions for robust monotonic convergence and optimal convergence speed in ILC design.

Findings

LMI feasibility conditions for robust convergence

Optimal ILC algorithm maximizing convergence speed

Flexible learning function order for design complexity

Abstract

This work investigates robust monotonic convergent iterative learning control (ILC) for uncertain linear systems in both time and frequency domains, and the ILC algorithm optimizing the convergence speed in terms of $l_{2}$ norm of error signals is derived. Firstly, it is shown that the robust monotonic convergence of the ILC system can be established equivalently by the positive definiteness of a matrix polynomial over some set. Then, a necessary and sufficient condition in the form of sum of squares (SOS) for the positive definiteness is proposed, which is amendable to the feasibility of linear matrix inequalities (LMIs). Based on such a condition, the optimal ILC algorithm that maximizes the convergence speed is obtained by solving a set of convex optimization problems. Moreover, the order of the learning function can be chosen arbitrarily so that the designers have the flexibility to decide the complexity of the learning algorithm.