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In this paper, we design an adaptive iterative learning control method for a class of high-order nonlinear output feedback discrete-time systems with random initial conditions and iteration-varying desired trajectories. Ann-step ahead predictor approach is employed to estimate future outputs. The discrete Nussbaum gain method is incorporated into the control design to deal with unknown control directions. The proposed control algorithm ensures that the tracking error converges to zero asymptotically along the iterative learning axis except for the beginning outputs affected by random initial conditions. A numerical simulation is carried out to demonstrate the efficacy of the presented control laws. [ABSTRACT FROM AUTHOR]