SGD-Based Adaptive NN Control Design for Uncertain Nonlinear Systems

In this paper, a stochastic gradient descent (SGD)-based adaptive neural network (NN) control scheme is presented for a class of uncertain nonlinear systems. The introduction of the SGD algorithm results in a better tracking performance compared with some other adaptive NN methods without using SGD. This is because the proposed SGD-based adaptive NN control strategy provides optimization algorithms for the weights, the widths, and the centers of the NNs, which can achieve a good function approximation performance. In order to implement the proposed method, extended differentiators are introduced to get the differential estimations of error signals, such that the loss function of the optimization algorithm can be constructed approximatively. Moreover, adaptive laws are designed to reduce the overall approximation errors, such that the tracking performance is further improved. By using the Lyapunov stability theory, it can be proved that the target signal is tracked by the system output within a small error. Finally, simulation and comparison results are given to show the effectiveness and advantages of the proposed method.