Adjustable-Error-Based Adaptive Neural Network Tracking Control for Uncertain Nonlinear Systems

This article proposes an adjustable-error neural network (NN) approximator and incorporates it into the adaptive neural tracking controller design of uncertain nonlinear systems. Noted that the error between the unknown nonlinear function and the NN approximator cannot be adjusted under the traditional NN control framework, as it is solely determined by the selection of neurons, basis functions, and the estimation of the ideal weight vector. This inherent constraint compromises the precision of the NN approximation and the convergence accuracy of the tracking error. To improve the approximation accuracy of unknown nonlinear functions in adaptive neural control systems, an adjustable-error NN approximator is designed, in which the error between the approximator and the unknown nonlinear function can be adjusted by designed parameters. Based on the proposed NN approximator, an adaptive neural tracking controller is designed for a class of uncertain nonlinear systems, which achieves higher accuracy of the tracking error compared with traditional methods. The stability of the resulting closed-loop system is proved in the Lyapunov sense, and the convergence of the tracking error is also analyzed. The effectiveness of the proposed scheme is verified by simulation and experiment.