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In this paper, robust adaptive output feedback control is studied for a class of discrete-time nonlinear systems in output-feedback form perturbed by a class of functional nonlinear uncertainties of Lipschitz type. To construct output feedback control, the system is transformed into the form of nonlinear-auto-regressive-moving-average (NARMA), a novel future output prediction is designed based on the NARMA model. With employment of the predicted future outputs, a constructive output feedback adaptive control is proposed with estimates of both parametric and functional nonlinear uncertainties. In the closed-loop system, the effect of the nonlinear uncertainties are completely compensated for such that the exact output tracking is achieved, while other closed-loop signals are guaranteed to be bounded. Simulation results are presented to show the effectiveness of the proposed approach.