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

• 成果类型: Article
• 署名作者: Zheng, Kangze; Li, Shuai; Zhang, Yunong
• 署名单位: Sun Yat Sen University; University of Oulu; VTT Technical Research Center Finland
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3319132
• 发表日期: 2024
• 页码: 4368-4379
• 关键词: Computational modeling; mathematical models; CONVERGENCE; Numerical models; Robustness; Nonlinear equations; nonlinear dynamical systems; Activation function (AF); dynamic nonlinear equation systems (DNESs); low computational complexity (LCC); trajectory following; zeroing neural network (ZNN)

摘要

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, the 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. In addition, 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.