A Novel Error-Based Adaptive Feedback Zeroing Neural Network for Solving Time-Varying Quadratic Programming Problems

Daxuan Yan, Chunquan Li, Junyun Wu (), Jinhua Deng, Zhijun Zhang, Junzhi Yu and Peter X. Liu
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Daxuan Yan: School of Information Engineering, Nanchang University, Nanchang 330031, China
Chunquan Li: School of Information Engineering, Nanchang University, Nanchang 330031, China
Junyun Wu: Jiangxi Provincial Key Laboratory of Intelligent Systems and Human-Machine Interaction, Nanchang 330031, China
Jinhua Deng: School of Information Engineering, Nanchang University, Nanchang 330031, China
Zhijun Zhang: School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640, China
Junzhi Yu: State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, BIC-ESAT, College of Engineering, Peking University, Beijing 100871, China
Peter X. Liu: Department of Systems and Computer Engineering, Carleton University, Ottawa, ON K1S 5B6, Canada

Mathematics, 2024, vol. 12, issue 13, 1-24

Abstract: This paper introduces a novel error-based adaptive feedback zeroing neural network (EAF-ZNN) to solve the time-varying quadratic programming (TVQP) problem. Compared to existing variable gain ZNNs, the EAF-ZNN dynamically adjusts the parameter to adaptively accelerate without increasing to very large values over time. Unlike adaptive fuzzy ZNN, which only considers the current convergence error, EAF-ZNN ensures regulation by introducing a feedback regulation mechanism between the current convergence error, the historical cumulative convergence error, the change rate of the convergence error, and the model gain parameter. This regulation mechanism promotes effective neural dynamic evolution, which results in high convergence rate and accuracy. This paper provides a detailed analysis of the convergence of the model, utilizing four distinct activation functions. Furthermore, the effect of changes in the proportional, integral, and derivative factors in the EAF-ZNN model on the rate of convergence is explored. To assess the superiority of EAF-ZNN in solving TVQP problems, a comparative evaluation with three existing ZNN models is performed. Simulation experiments demonstrate that the EAF-ZNN model exhibits a superior convergence rate. Finally, the EAF-ZNN model is compared with the other three models through the redundant robotic arms example, which achieves smaller position error.

Keywords: time-varying quadratic programming (TVQP); adaptive parameter; convergence analysis; zeroing neural network (ZNN); PID control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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