For a class of nonlinear systems, a new learning control algorithm is proposed, which increases iterative learning
rule of initial state of system on the base of iterative learning control with variable learning gain. By using the operator
theory, it is proved that the output of system can track the expected trajectory completely after the iterative learning of system
with initial state disturbance, and the convergent condition for the spectral radius form of the algorithm is given. Compared
with the tranditional iterative learning control, the proposed algorithm not only significantly improves the convergent speed,
but also solves the initial state disturbance problem of the iterative learning control with variable learning gain. Simulation
results show the effectiveness of the proposed algorithm.

nonlinear system;iterative learning control;state study;variable learning gain;operator theory