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

• Published in: IEEE transaction on neural networks and learning systems Vol. 34; no. 1; pp. 305 - 315
• Main Authors: Wang, Yujia, Wang, Tong, Yang, Xuebo, Yang, Jiae
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.01.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Artificial neural networks; Closed loop systems; Closed loops; Control systems design; Controllers; Convergence; Cost function; Discrete time systems; Feedback control; Gradient descent-Barzilai Borwein (GD-BB); Heuristic algorithms; Machine learning; Neural networks; neural networks (NNs); Nonlinear control; Nonlinear dynamical systems; Nonlinear systems; Parameters; Process control; Radial basis function; Stability analysis; Theoretical analysis; Tracking control; unknown dynamics
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2021.3093877

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.