2-D analysis based iterative learning control for linear discrete-time systems with time delay
type: Item
instance of: scholarly article
title: 2-D analysis based iterative learning control for linear discrete-time systems with time delay
zbMATH Open document ID: 1228.93074
author: Chuandong Li
author: Fali Ma
author: Tingwen Huang
published in: Journal of Industrial and Management Optimization
publication date: 2011-06-10T00:00:00Z
review text: Iterative Learning Control (ILC) technique, based on the theory of two-dimensional (2-D) systems, is well developed for linear continuous time-delay systems and linear discrete-time systems. Grounded on the 2-D linear continuous-discrete Roesser's model, the ILC process is investigated in the paper for linear discrete-time systems with constant time delay \[ x(t+1) = Ax(t)+A_1x(t-\tau)+Bu(t), \qquad y(t)=Cx(t)+Du(t), \] where \(t \in T_0 = \{0, 1, \dots , T\}\), \(x(t) \in\mathbb R^n\) is the state vector, \(u(t) \in\mathbb R^m\) is the input vector, and \(y(t) \in\mathbb R^p\) is the output vector. A sufficient condition is obtained providing that the system output \(y(t,k)\) converges asymptotically to the reference trajectory \(y_r(t)\) under the proposed ILC rule \(u(t, k+1)= u(t, k) + K e(t, k)\), i.e., \(e(t, k)= y_r(t) - y(t,k) \to 0\) when \(k \to \infty\). Numerical results are presented to illustrate the proposed scheme.
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 37N35
Mathematics Subject Classification ID: 39A60
Mathematics Subject Classification ID: 68T05
zbMATH DE Number: 5906859
zbMATH Keywords: iterative learning control
zbMATH Keywords: 2-D system theory
zbMATH Keywords: linear discrete-time system
zbMATH Keywords: time delay
Wikidata QID: Q61891287
MaRDI profile type: Publication
full work available at URL: jimo.2011.7.175
OpenAlex ID: W2314440012
DOI: 10.3934/JIMO.2011.7.175
description: scientific article; zbMATH DE number 5906859