Adaptive control of discrete-time nonlinear systems by recurrent neural networks in a Quasi Sliding mode regime

The control problem of nonlinear systems affected by external perturbations and parametric uncertainties has attracted the attention for many researches. Artificial Neural Networks (ANN) constitutes an option for systems whose mathematical description is uncertain or partially unknown. In this paper, a Recurrent Neural Network (RNN) is designed to address the problems of identification and control of discrete-time nonlinear systems given by a gray box. The learning laws for the RNN are designed in terms of discrete-time Lyapunov stability. The control input is developed fulfilling the existence condition to establish a Quasi Sliding Regime. In means of Lyapunov stability, the identification and tracking errors are ultimately bounded in a neighborhood around zero. Numerical examples are presented to show the behavior of the RNN in the identification and control processes of a highly nonlinear discrete-time system, a Lorentz chaotic oscillator.