Initial shift problem for robust iterative learning control systems with polytopic-type uncertainty

Abstract

This article deals with the initial shift problem of robust iterative learning control (ILC) for uncertain continuous-time systems. Two ILC laws are considered by the two-dimensional (2-D) analysis approach. It is shown that a necessary and sufficient convergence condition can be directly derived using the theory of 2-D systems. It is also shown that if the system parameters are subject to polytopic-type uncertainties, this convergence condition can induce a sufficient condition for the robust ILC convergence. Furthermore, the 2-D analysis approach can be extended to address the initial shift problem of robust ILC for multiple-input–multiple-output, uncertain time-delay systems. Two numerical simulation examples are provided to illustrate the theoretical results.

Keywords:

• iterative learning control
• initial shift
• continuous-time systems
• time delays
• 2-D analysis approach

Acknowledgements

This work was supported by the NSFC (Nos. 60727002, 60774003, 60921001 and 90916024), the MOE (No. 20030006003), the COSTIND (No. A2120061303), the National 973 Program (No. 2005CB321902) and the Innovation Foundation of BUAA for PhD Graduates. The authors would like to thank the anonymous reviewers for their constructive comments which improved the presentation of this article.