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The tracking control problem for a class of nonaffne uncertain discrete-time nonlinear systems is addressed. Firstly, a linear output feedback dynamic compensator is proposed to stabilize the linear portion of the tracking error system, and a discrete single-hidden-layer (SHL) neural network (NN) controller is introduced to cancel the inversion error. NN learn though the recursive weight update rules that are derived from the discrete-time version of Lyapunov control theory. Secondly, a linear observer is proposed for the tracking error dynamics. Thirdly, by the Lyapunov stability theory, we show that the output tracking error converges to a neighborhood of the origin, whose size can be adjusted by control parameters. Finally, simulation illustrates the effectiveness of the proposed control method.