Robust identification for singularly perturbed nonlinear systems using multi-time-scale dynamic neural network

In this paper, a novel identification scheme is proposed for a class of singularly perturbed nonlinear systems. In order to identify the unknown singularly perturbed nonlinear system, a set of filtered variables are firstly defined and incorporated into the multi-time-scale dynamic neural network (DNN). Subsequently, the new weight's updating laws are proposed to train the neural network, such that the neural network weights will converge to their nominal values. By incorporating the filtered variables into the dynamic neural network, the derivatives of the identification errors are no longer needed in the weight's updating laws. As a result, the identification scheme proposed here is more robust to the measurement noises. The stability analysis of the identification algorithm using Lyapunov method is presented. Numerical simulations are performed to demonstrate the validity of the proposed identification algorithm.