Abstract: For a class of discrete nonlinear repeated systems with random input and output disturbances, we propose an open-closed loop P-type robust iterative learning trajectory tracking control algorithm for cases in which the initial states are not strictly identical to given expected values. Based on the λ norm theory, we prove the robust stability of the iterative learning algorithm, and optimize the gain matrix parameters of the P-type open-closed control law based on the performance of the multiple objective function. In this way, the monotonic convergence of the trajectory output tracking error can be guaranteed by the optimization algorithm, which improves the convergence speed and tracking accuracy. Lastly, our simulation results of a mobile robot in two-dimensional motion show the effectiveness and feasibility of the proposed algorithm.