Multiple Estimation Models for Discrete-time Adaptive Iterative Learning Control

TL;DR

This paper introduces a novel discrete-time adaptive iterative learning control strategy utilizing multiple estimation models and the last component of the identification error, leading to bounded and convergent errors without relying on a key technical lemma.

Contribution

It proposes a new adaptive ILC method with multiple models and a unique error-based tuning strategy, improving convergence speed and robustness.

Findings

Bounded parameter estimates and errors achieved.

Convergence of signals demonstrated.

Faster convergence shown through simulations.

Abstract

This article focuses on making discrete-time Adaptive Iterative Learning Control (ILC) more effective using multiple estimation models. Existing strategies use the tracking error to adjust the parametric estimates. Our strategy uses the last component of the identification error to tune these estimates of the model parameters. We prove that this strategy results in bounded estimates of the parameters, and bounded and convergent identification and tracking errors. We emphasize that the proof does not use the key technical lemma. Rather, it uses the properties of square-summable sequences. We extend this strategy to include multiple estimation models and show that all the signals are bounded, and the errors converge. It is also shown that this works whether we switch between the models at every instant and every iteration or at the end of every iteration. Simulation results demonstrate the efficacy of the proposed method with a faster convergence using multiple estimation models.