Data-Driven Tracking Control Based on LM and PID Neural Network With Relay Feedback for Discrete Nonlinear Systems

Abstract

In this article, a hybrid algorithm of Levenberg-Marquardt (LM) and proportional-integral-derivative neural network (PIDNN) with the relay feedback (LM-PIDNN-RF) is proposed to solve control problems for unknown discrete nonlinear systems. First, the PIDNN is initialized by the relay feedback to solve the problem of assigning initial weights; meanwhile, the LM neural network is regarded as an identifier to fit system input/output quickly and accurately. Second, the partial derivative of the system output to system input is transferred to the PIDNN, which ensures that the weights of the PIDNN can be updated correctly in time. The hybrid algorithm can update the weights of the neural network controller correctly against the errors caused by system instantaneous disturbance, and the controller has only one parameter to be tuned manually. Moreover, the stability of the closed-loop system is proven by using the Lyapunov stability theory. The proposed hybrid algorithm can significantly improve tracking performance in comparison with PIDNN and RF-PID. The results of three simulation examples and a physical experiment are presented to show superior tracking performance of the proposed algorithm.