System Equivalence Transformation: Robust Convergence of Iterative Learning Control with Nonrepetitive Uncertainties

TL;DR

This paper introduces a system equivalence transformation (SET) that enables robust convergence analysis of iterative learning control (ILC) systems with nonrepetitive uncertainties, simplifying the conditions needed for convergence and boundedness.

Contribution

The paper proposes a novel system equivalence transformation (SET) that transforms general MIMO systems into a specific class, facilitating unified convergence conditions for ILC with uncertainties.

Findings

Unified condition guarantees convergence and boundedness.

SET simplifies analysis of nonrepetitive uncertainties.

Simulation confirms robustness of the proposed ILC method.

Abstract

For iterative learning control (ILC), one of the basic problems left to address is how to solve the contradiction between convergence conditions for the output tracking error and for the input signal (or error). This problem is considered in the current paper, where the robust convergence analysis is achieved for ILC systems in the presence of nonrepetitive uncertainties. A system equivalence transformation (SET) is proposed for ILC such that given any desired reference trajectories, the output tracking problems for general nonsquare multi-input, multi-output (MIMO) systems can be equivalently transformed into those for the specific class of square MIMO systems with the same input and output channels. As a benefit of SET, a unified condition is only needed to guarantee both the uniform boundedness of all system signals and the robust convergence of the output tracking error, which avoids causing the condition contradiction problem in implementing the double-dynamics analysis approach to ILC. Simulation examples are included to demonstrate the validity of our established robust ILC results.