Open Access

ARTICLE

Robustness Convergence for Iterative Learning Tracking Control Applied to Repetitfs Systems

Ben Attia Selma^*, Ouerfelli Houssem Eddine, Salhi Salah

Laboratory of Analysis, Conception and Control of Systems (LACCS), University of Tunis El Manar, Tunis, 1002, Tunisia

* Corresponding Author: Ben Attia Selma. Email:

Intelligent Automation & Soft Computing 2022, 32(2), 795-810. https://doi.org/10.32604/iasc.2022.020435

Received 24 May 2021; Accepted 22 July 2021; Issue published 17 November 2021

Abstract

This study addressed sufficient conditions for the robust monotonic convergence of repetitive discrete-time linear parameter varying systems, with the parameter variation rate bound. The learning law under consideration is an anticipatory iterative learning control. Of particular interest in this study is that the iterations can eliminate the influence of disturbances. Based on a simple quadratic performance function, a sufficient condition for the proposed learning algorithm is presented in terms of linear matrix inequality (LMI) by imposing a polytopic structure on the Lyapunov matrix. The set of LMIs to be determined considers the bounds on the rate of variation of the scheduling parameter. The control law designs polynomial ILC by constructing a sequence of control inputs to a discrete-time R-LPV system, producing an iterative dynamic for the R-LPV system with respect to the polytopic structure for uncertain parameters. Numerical simulations were performed to demonstrate the benefits of the proposed technique.

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Keywords

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