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Using the properties of universal approximation of multilayer perceptron neural networks, a class of discrete nonlinear dynamical systems are modeled by a perceptron with two hidden layers. The authors' backpropagation algorithm is then used to train the model to identify the nonlinear systems to a desired degree of accuracy. Based on the identified model, a one step ahead predictive control scheme is proposed in which the future control inputs are obtained through some nonlinear optimization process. Making use of the online learning properties of neural networks, the predictive control scheme is further developed into an adaptive one which is robust to the incompleteness of identification. Simulation results show that the control scheme works well even for some very complicated nonlinear systems.