Gradient Descent-Barzilai Borwein-Based Neural Network Tracking Control for Nonlinear Systems With Unknown Dynamics

In this article, a combined gradient descent-Barzilai Borwein (GD-BB) algorithm and radial basis function neural network (RBFNN) output tracking control strategy was proposed for a family of nonlinear systems with unknown drift function and control input gain function. In such a method, a neural network (NN) is used to approximate the controller directly. The main merits of the proposed strategy are given as follows: first, not only the NN parameters, such as weights, centers, and widths but also the learning rates of NN parameter updating laws are updated online via the proposed learning algorithm based on Barzilai-Borwein technique; and second, the controller design process can be further simplified, the controller parameters that should be tuned can be greatly reduced. Theoretical analysis about the stability of the closed-loop system is manifested. In addition, simulations were conducted on a numerical discrete time system and an inverted pendulum system to validate the presented control strategy.