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A new robust adaptive control algorithm is developed for a class of uncertain discrete-time SISO systems. Different from the existing investigated systems, the concerned discrete system here is with both uncertain smooth nonlinear functions and unknown disturbance. On the basis of the idea of neural network (NN) approximation, a novel recurrent neural network (RNN) is first proposed and used to approximate a backstepping control law following the transformation of the original system into a predictor form. According to Lyapunov stability theorem, a new on-line tuning law for parameters of RNN  is obtained. Meanwhile, in order to achieve satisfying robust tracking performance, a novel controller is constructed by virtue of the approximation error of RNN. It has been proved that all the concerned signals are uniformly ultimately bounded. In addition, a very small tracking error can be obtained through appropriate selection of control parameters. Finally, we give a simulation example to demonstrate the validness of the newly proposed control algorithm for the investigated systems.

Adaptive control for uncertain discrete-time systems with unknown disturbance based on RNN