Low-Computational-Complexity Zeroing Neural Network Model for Solving Systems of Dynamic Nonlinear Equations

Abstract – Nonlinear equation systems are ubiquitous in a variety of fields, and how to tackle them has drawn much attention, especially dynamic ones. As a particular class of recurrent neural network, zeroing neural network (ZNN) takes time-derivative information into consideration, and thus, is a competent approach to dealing with dynamic problems. Hitherto, two kinds of ZNN models have been developed for solving systems of dynamic nonlinear equations. One of them is explicit, involving the computation of a pseudoinverse matrix, and the other is of implicit dynamics essentially. To address these two issues at once, a low-computational-complexity ZNN (LCCZNN) model is proposed. It does not need to compute any pseudoinverse matrix, and is in the form of explicit dynamics. Additionally, a novel activation function is presented to endow the LCCZNN model with finite-time convergence and certain robustness, which is proved rigorously by Lyapunov theory. Numerical experiments are conducted to validate the results of theoretical analyses, including the competence and robustness of the LCCZNN model. Finally, a pseudoinverse-free controller derived from the LCCZNN model is designed for a UR5 manipulator to online accomplish a trajectory-following task.

Index Terms – Low computational complexity, activation function, zeroing neural network, dynamic nonlinear equation systems, trajectory following.