Adaptive Control based on Extended Neural Network for SISO Uncertain Nonlinear Systems

This paper proposes a novel adaptive control criterion for a class of single-input-single-output (SISO) uncertain nonlinear systems by using extended neural networks (ENNs). Distinguished from the traditional neural networks, our ENNs are composed of radial basis function neural networks (RBFNNs), scalers and saturators. And these ENNs are used to approximate the uncertainties in the nonlinear systems. Based on the Lyapunov stability theory and our ENNs, an adaptive control scheme is designed to guarantee that all the signals in the closed-loop system are uniformly ultimately bounded (UUB). It is also worth pointing out that our control method makes the construction of RBFNNs and the design of adaptive laws separated, which means only the outputs of ENNs and one update law of the parameter in the scaler are to be adjusted. Thus, our control scheme can effectively reduce the online computation burden of the adaptive parameters. Finally, simulation examples are given to verify the effectiveness of our theoretical result.