用于有界噪声时变矩阵计算的终端零化神经网络

仲国民; 唐逸飞; 孙明轩

doi:10.11959/j.issn.1000-436x.2024166

您当前的位置：

首页 >

文章列表页 >

用于有界噪声时变矩阵计算的终端零化神经网络

学术论文 | 更新时间：2024-10-10

- 用于有界噪声时变矩阵计算的终端零化神经网络
- Terminal zeroing neural network for time-varying matrix computing under bounded noise
- 通信学报 2024年45卷第9期页码：55-67
- 作者机构：
  
  浙江工业大学信息工程学院，浙江杭州 310023
- 作者简介：
  
  [ "仲国民（1983- ），男，浙江杭州人，博士，浙江工业大学讲师，主要研究方向为系统辨识、迭代学习控制和神经计算。" ]
  [ "唐逸飞（2000- ），男，浙江杭州人，浙江工业大学硕士生，主要研究方向为系统辨识和神经计算。" ]
  [ "孙明轩（1961- ），男，安徽蚌埠人，博士，浙江工业大学教授，主要研究方向为学习系统和神经计算等。" ]
- 基金信息：
  
  国家自然科学基金资助项目(62073291;62222315);浙江省自然科学基金资助项目(LZ22F030007)
- DOI：10.11959/j.issn.1000-436x.2024166
  中图分类号： TP183
- 收稿日期：2024-03-11，
  
  修回日期：2024-08-27，
  
  纸质出版日期：2024-09-25
- 稿件说明：
移动端阅览
仲国民,唐逸飞,孙明轩.用于有界噪声时变矩阵计算的终端零化神经网络[J].通信学报,2024,45(09):55-67.

ZHONG Guomin,TANG Yifei,SUN Mingxuan.Terminal zeroing neural network for time-varying matrix computing under bounded noise[J].Journal on Communications,2024,45(09):55-67.
仲国民,唐逸飞,孙明轩.用于有界噪声时变矩阵计算的终端零化神经网络[J].通信学报,2024,45(09):55-67. DOI： 10.11959/j.issn.1000-436x.2024166.

ZHONG Guomin,TANG Yifei,SUN Mingxuan.Terminal zeroing neural network for time-varying matrix computing under bounded noise[J].Journal on Communications,2024,45(09):55-67. DOI： 10.11959/j.issn.1000-436x.2024166.

摘要

为提升零化神经网络（ZNN）求解时变矩阵计算问题时的收敛性能，提出一种具有抗噪能力的终端零化神经网络（TZNN）及其对数加速形式（LA-TZNN）。对误差动态的终态吸引性展开分析，结果表明所提网络在受到有界噪声干扰时仍能在固定时间内使误差归零，其中LA-TZNN可实现对数调节时间稳定，收敛速度相较于TZNN更快。考虑到实际情况中初始误差有界，给出半全局意义上的调节时间上界，并通过设置可调参数，使网络实现预定义时间稳定。将2种模型应用于时变矩阵求逆和PUMA560机械臂重复运动规划问题，仿真结果验证了所提方法相较于传统ZNN设计，调节时间更短，收敛精度更高，并能够有效抑制有界噪声干扰。

Abstract

To improve the convergence performance of zeroing neural network (ZNN) for time-varying matrix computation problems solving

a terminal zeroing neural network (TZNN) with noise resistance and its logarithmically accelerated form (LA-TZNN) were proposed. The terminal attraction of the error dynamic equation were analyzed

and the results showed that the neural state of the proposed networks can converge to the theoretical solution within a fixed time when subjected to bounded noises. In addition

the LA-TZNN could achieve logarithmical settling-time stability

and its convergence speed was faster than the TZNN. Considering that the initial error was bounded in actual situations

an upper bound of the settling-time in a semi-global sense was given

and an adjustable parameter was set to enable the network to converge within a predefined time. The two proposed models were applied to solve the time-varying matrix inversion and trajectory planning of redundant manipulators PUMA560. The simulation results further verified that compared with the conventional ZNN design

the proposed methods have shorter settling-time

higher convergence accuracy

and can effectively suppress bounded noise interference.

关键词

Keywords

references

MARCOS M D G , MACHADO J A T , AZEVEDO-PERDICOÚLIS T P . A multi-objective approach for the motion planning of redundant manipulators [J ] . Applied Soft Computing , 2012 , 12 ( 2 ): 589 - 599 .

ZHU W P , AHMAD M O , SWAMY M N S . Weighted least-square design of FIR filters using a fast iterative matrix inversion algorithm [J ] . IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications , 2002 , 49 ( 11 ): 1620 - 1628 .

NAZEMI A , NAZEMI M . A gradient-based neural network method for solving strictly convex quadratic programming problems [J ] . Cognitive Computation , 2014 , 6 ( 3 ): 484 - 495 .

ZHANG Y N , GE S S . Design and analysis of a general recurrent neural network model for time-varying matrix inversion [J ] . IEEE Transactions on Neural Networks , 2005 , 16 ( 6 ): 1477 - 1490 .

GUO D S , YI C F , ZHANG Y N . Zhang neural network versus gradient-based neural network for time-varying linear matrix equation solving [J ] . Neurocomputing , 2011 , 74 ( 17 ): 3708 - 3712 .

MIAO P , ZHENG Y H , LI S . A new FXTZNN model for solving TVCS equation and application to pseudo-inverse of a matrix [J ] . Applied Mathematics and Computation , 2024 , 465 : 128409 .

XIAO L , TAO J , LI W B . An arctan-type varying-parameter ZNN for solving time-varying complex sylvester equations in finite time [J ] . IEEE Transactions on Industrial Informatics , 2022 , 18 ( 6 ): 3651 - 3660 .

ZUO Q Y , LI K L , XIAO L , et al . On generalized zeroing neural network under discrete and distributed time delays and its application to dynamic Lyapunov equation [J ] . IEEE Transactions on Systems, Man, and Cybernetics: Systems , 2022 , 52 ( 8 ): 5114 - 5126 .

JIN J , CHEN W J , CHEN C Y , et al . A predefined fixed-time convergence ZNN and its applications to time-varying quadratic programming solving and dual-arm manipulator cooperative trajectory tracking [J ] . IEEE Transactions on Industrial Informatics , 2023 , 19 ( 8 ): 8691 - 8702 .

DAI L Y , ZHANG Y Y , GENG G G . Norm-based finite-time convergent recurrent neural network for dynamic linear inequality [J ] . IEEE Transactions on Industrial Informatics , 2024 , 20 ( 3 ): 4874 - 4883 .

ZHANG Y N , LI W B , ZHANG Z J . Physical-limits-constrained minimum velocity norm coordinating scheme for wheeled mobile redundant manipulators [J ] . Robotica , 2015 , 33 ( 6 ): 1325 - 1350 .

LI W B , MA X , LUO J W , et al . A strictly predefined-time convergent neural solution to equality- and inequality-constrained time-variant quadratic programming [J ] . IEEE Transactions on Systems, Man, and Cybernetics: Systems , 2021 , 51 ( 7 ): 4028 - 4039 .

DAI J H , CAO Y K , XIAO L , et al . Design and analysis of a noise-suppression zeroing neural network approach for robust synchronization of chaotic systems [J ] . Neurocomputing , 2021 , 426 ( 5 ): 299 - 308 .

LUO J J , XIAO L , CAO P L , et al . A new class of robust and predefined-time consensus protocol based on noise-tolerant ZNN models [J ] . Applied Soft Computing , 2023 , 145 : 110550 .

ZHANG Y N , JIANG D C , WANG J . A recurrent neural network for solving Sylvester equation with time-varying coefficients [J ] . IEEE Transactions on Neural Networks , 2002 , 13 ( 5 ): 1053 - 1063 .

XIAO L , JIA L . Zeroing neural networks: finite-time convergence design, analysis and applications [M ] . New Jersey : John Wiley & Sons, Inc. , 2022 .

SUN M X , ZHANG Y , WU Y X , et al . On a finitely activated terminal RNN approach to time-variant problem solving [J ] . IEEE Transactions on Neural Networks and Learning Systems , 2022 , 33 ( 12 ): 7289 - 7302 .

SÁNCHEZ-TORRES J D , SANCHEZ E N , LOUKIANOV A G . Predefined-time stability of dynamical systems with sliding modes [C ] // Proceedings of the 2015 American Control Conference (ACC) . Piscataway : IEEE Press , 2015 : 5842 - 5846 .

XIAO L , ZHANG Y S , HU Z S , et al . Performance benefits of robust nonlinear zeroing neural network for finding accurate solution of Lyapunov equation in presence of various noises [J ] . IEEE Transactions on Industrial Informatics , 2019 , 15 ( 9 ): 5161 - 5171 .

KONG Y , WU J J , JIANG Y L , et al . Robust terminal recurrent neural network for finding exact solution of the TVQP problem with various noises [J ] . IEEE Transactions on Industrial Informatics , 2023 , 19 ( 5 ): 6907 - 6916 .

LI S , LI Y M . Nonlinearly activated neural network for solving time-varying complex sylvester equation [J ] . IEEE Transactions on Cybernetics , 2014 , 44 ( 8 ): 1397 - 1407 .

QI Z H , NING Y Q , XIAO L , et al . Predefined-time zeroing neural networks with independent prior parameter for solving time-varying plural Lyapunov tensor equation [J ] . IEEE Transactions on Neural Networks and Learning Systems , 2024 , 35 ( 7 ): 9408 - 9416 .

LI W B , GUO C , MA X , et al . A strictly predefined-time convergent and noise-tolerant neural model for solving linear equations with robotic applications [J ] . IEEE Transactions on Industrial Electronics , 2024 , 71 ( 1 ): 798 - 809 .

ZHANG Z J , ZHENG L N , QIU T R , et al . Varying-parameter convergent-differential neural solution to time-varying overdetermined system of linear equations [J ] . IEEE Transactions on Automatic Control , 2020 , 65 ( 2 ): 874 - 881 .

DAI J H , TAN P , XIAO L , et al . A fuzzy adaptive zeroing neural network model with event-triggered control for time-varying matrix inversion [J ] . IEEE Transactions on Fuzzy Systems , 2023 , 31 ( 11 ): 3974 - 3983 .

XIAO L , HE Y J . A noise-suppression ZNN model with new variable parameter for dynamic sylvester equation [J ] . IEEE Transactions on Industrial Informatics , 2021 , 17 ( 11 ): 7513 - 7522 .

ZHANG Z J , ZHENG L N , WENG J , et al . A new varying-parameter recurrent neural-network for online solution of time-varying sylvester equation [J ] . IEEE Transactions on Cybernetics , 2018 , 48 ( 11 ): 3135 - 3148 .

JIN L , ZHANG Y N , LI S . Integration-enhanced Zhang neural network for real-time-varying matrix inversion in the presence of various kinds of noises [J ] . IEEE Transactions on Neural Networks and Learning Systems , 2016 , 27 ( 12 ): 2615 - 2627 .

李建锋 , 刘哲宇 , 荣洋 , 等 . 用于线性噪声时变凸二次规划的归零神经网络 [J ] . 通信学报 , 2023 , 44 ( 4 ): 226 - 233 .

LI J F , LIU Z Y , RONG Y , et al . Zeroing neural network for time-varying convex quadratic programming with linear noise [J ] . Journal on Communications , 2023 , 44 ( 4 ): 226 - 233 .

XIAO L , CAO P L , SONG W T , et al . A fixed-time noise-tolerance ZNN model for time-variant inequality-constrained quaternion matrix least-squares problem [J ] . IEEE Transactions on Neural Networks and Learning Systems , 2024 , 35 ( 8 ): 10503 - 10512 .

HU Z S , LI K L , XIAO L , et al . Adams-bashforth-type discrete-time zeroing neural networks solving time-varying complex sylvester equation with enhanced robustness [J ] . IEEE Transactions on Systems, Man, and Cybernetics: Systems , 2022 , 52 ( 5 ): 3287 - 3298 .

XIAO L , ZHANG Y S , DAI J H , et al . A new noise-tolerant and predefined-time ZNN model for time-dependent matrix inversion [J ] . Neural Networks , 2019 , 117 : 124 - 134 .

JIN J , ZHU J C , ZHAO L , et al . A robust predefined-time convergence zeroing neural network for dynamic matrix inversion [J ] . IEEE Transactions on Cybernetics , 2023 , 53 ( 6 ): 3887 - 3900 .

LI X , WANG L M , ZHONG G M , et al . Fixed-time convergent RNNs with logarithmic settling time for time-variant quadratic programming solving with application to repetitive motion planning [J ] . Neural Computing and Applications , 2024 , 36 ( 1 ): 445 - 460 .

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

暂无数据