Gradient-Feedback Zhang Neural Network for Unconstrained Time-Variant Convex Optimization and Robot Manipulator Application

Optimization problems are frequently encountered in various fields. In this article, the unconstrained time-variant convex optimization (UTVCO) problem is investigated. Generally, gradient neural network (GNN) is a traditional and effective method for solving time-invariant problems by making use of the gradient information. However, GNN is less effective on time-variant problems. On the other hand, Zhang neural network (ZNN) performs well on time-variant problems by exploiting the time-derivative information. In order to solve the UTVCO problem effectively and quickly with the help of the gradient information, inspired by the two methods, gradient-feedback ZNN (GZNN) is presented by taking both advantages of GNN and ZNN to solve the UTVCO problem. The main contributions are presented as follows. 1) The GZNN model for solving the UTVCO problem is proposed and analyzed theoretically. 2) Comparisons among GZNN, ZNN, GNN, and other models are presented with detailed discussions. Suggestions are provided on how to choose a model for solving the UTVCO problem better. 3) Tracking control of the robot manipulator is formulated as a UTVCO problem and studied with the GZNN model. According to the simulative and physical experiments, the task of tracking control is accomplished excellently by using the GZNN model.