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Title: Robust optimal design and convergence properties analysis of iterative learning control approaches
Authors: Xu, J.-X. 
Tan, Y.
Keywords: Convergence speed
Convergence speed comparison
Dynamic impact
Higher-order ILC scheme
Robust optimal design
Issue Date: Nov-2002
Citation: Xu, J.-X.,Tan, Y. (2002-11). Robust optimal design and convergence properties analysis of iterative learning control approaches. Automatica 38 (11) : 1867-1880. ScholarBank@NUS Repository.
Abstract: In this paper, we address four major issues in the field of iterative learning control (ILC) theory and design. The first issue is concerned with ILC design in the presence of system interval uncertainties. Targeting at time-optimal (fastest convergence) and robustness properties concurrently, we formulate the ILC design into a min-max optimization problem and provide a systematic solution for linear-type ILC consisting of the first-order and higher-order ILC schemes. Inherently relating to the first issue, the second issue is concerned with the performance evaluation of various ILC schemes. Convergence speed is one of the most important factors in ILC. A learning performance index -- Q-factor -- is introduced, which provides a rigorous and quantified evaluation criterion for comparing the convergence speed of various ILC schemes. We further explore a key issue: how does the system dynamics affect the learning performance. By associating the time weighted norm with the supreme norm, we disclose the dynamics impact in ILC, which can be assessed by global uniform bound and monotonicity in iteration domain. Finally we address a rather controversial issue in ILC: can the higher-order ILC outperform the lower-order ILC in terms of convergence speed and robustness? By applying the min-max design, which is robust and optimal, and conducting rigorous analysis, we reach the conclusion that the Q-factor of ILC sequences of lower-order ILC is lower than that of higher-order ILC in terms of the time-weighted norm. © 2002 Elsevier Science Ltd. All rights reserved.
Source Title: Automatica
ISSN: 00051098
DOI: 10.1016/S0005-1098(02)00143-7
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