Robust optimal design and convergence properties analysis of iterative learning control approaches

In this paper, we address four major issues in the field of iterative learning control (TLC) theory and design. The first issue is concerned with TLC design in the presence of system interval uncertainties. Targeting at time-optimal (fastest convergence) and robustness properties concurrently, we formulate the TLC design into a min-max optimization problem and provide a systematic solution for linear-type TLC consisting of the first-order and higher-order TLC schemes. Inherently relating to the first issue, the second issue is concerned with the performance evaluation of various TLC schemes. Convergence speed is one of the most important factors in TLC. A learning performance index-Q-factor-is introduced, which provides a rigorous and quantified evaluation criterion for comparing the convergence speed of various TLC 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 TLC, which can be assessed by global uniform bound and monotonicity in iteration domain. Finally we address a rather controversial issue in TLC: can the higher-order TLC outperform the lower-order TLC 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 TLC sequences of lower-order TLC is lower than that of higher-order TLC in terms of the time-weighted norm, (C) 2002 Elsevier Science Ltd. All rights reserved.