1.College of Information Engineering, Zhejiang University of Technology, Hangzhou 310014, China; 
2.School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639794; 
3.Department of Mathematics, China Institute of Metrology, Hangzhou 310018, China

Iterative learning control requires initial repositioning, while the time functions to be learned should be of periodicity in repetitive control. However, there are cases in practice where the time-varying unknowns are not periodic but repetitive, and repetitive learning control is applicable with avoidance of initial repositioning. In this paper, repetitive learning control designs are presented for a broader class of nonlinear systems over finite intervals. The Freeman formula is modified and used for stabilization of the nominal nonlinear time-varying system undertaken. The global stability of the learning system and asymptotic convergence of the tracking error are established through analysis of both partially and fully saturated learning algorithms, respectively. The repetitive learning control method is theoretically shown to be effective in dealing with time-varying parametric uncertainties.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 60474005, 60874041), the Natural Science Foundation of Zhejiang Province (Grant No. Y107494), and the Scientific Research Founda- tion for the Returned Overseas Chinese Scholars, State Education Ministry.