Abstract: For a class of uncertain nonlinear time-varying systems with arbitrary initial states and aperiodic bounded disturbance，an iterative learning control (ILC) method on the basis of boundary layer is presented． In this me-thod，boundary layer is designed as a decaying exponential function with residual width，the arbitrary initial state problem of ILC is transformed into a zero initial state problem by the designed boundary layer，and learning laws of periodic and aperiodic terms are designed for periodic and aperiodic disturbances，respectively． On the basis of these two laws，an ILC algorithm is presented，and the corresponding theorem is given with detail proof through Lyapunov-like approach． Simulated results show that the proposed algorithm is effective and is capable of conver-ging trajectory tracking errors to boundary layer．

Key words: uncertain system, iterative learning control, initial state problem, boundary layer, Lyapunov-like approach