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| 梯度神经网络解线性矩阵方程之收敛性分析 | |
| 引用本文： | 张雨浓,史艳燕,蔡炳煌,张禹珩,陈轲.梯度神经网络解线性矩阵方程之收敛性分析[J].控制工程,2012,19(2):235-239. |
| 作者姓名： | 张雨浓 史艳燕 蔡炳煌 张禹珩 陈轲 |
| 作者单位： | 1. 中山大学信息科学与技术学院,广东广州,510006 2. 朱拉隆功大学工学院,泰国曼谷10330 3. 伦敦大学玛丽女王学院计算机科学学院,伦敦英国E1 4NS |
| 基金项目： | 中国国家自然科学基金(61075121,60935001) |
| 摘 要： | 为了求解线性矩阵方程问题,应用一种基于负梯度法的递归神经网络模型,并探讨了该递归神经网络实时求解线性矩阵方程的全局指数收敛问题.在讨论渐近收敛性基础上,进一步证明了该类神经网络在系数矩阵满足有解条件的情况下具有全局指数收敛性,在不能满足有解条件的情况下具有全局稳定性.计算机仿真结果证实了相关理论分析和该网络实时求解线性矩阵方程的有效性. |
| 关 键 词： | 梯度神经网络(GNN) 线性矩阵方程 李氏稳定性定理 全局指数收敛 渐近收敛 |
Convergence Analysis of Gradient Neural Network Solving Linear Matrix Equations |
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| ZHANG Yu-nong , SHI Yan-yan , CAI Bing-huang , ZHANG Yu-heng , CHEN Ke.Convergence Analysis of Gradient Neural Network Solving Linear Matrix Equations[J].Control Engineering of China,2012,19(2):235-239. | |
| Authors: | ZHANG Yu-nong SHI Yan-yan CAI Bing-huang ZHANG Yu-heng CHEN Ke |
| Affiliation: | 1.School of Information Science & Technology Sun Yat-Sen University,Guangzhou 510006,China; 2.Faculty of Engineering Chulalongkorn University,Bangkok 10330,Thailand; 3.Department of Computer Science Queen Mary University of London London,E1 4NS,United Kingdom.) |
| Abstract: | To solve the problem of linear matrix equations,a type of negative-gradient based recurrent neural network is applied,and its global exponential convergence is investigated for the online solution.Base on the discussion of asymptotical convergence,global exponential convergence(when the coefficients satisfy a unique-solution condition) and global stability(when the coefficients do not satisfy such a condition) of GNN are proved further.Computer-simulation results substantiate the related theoretical analysis and efficacy of the neural network on solving online linear matrix equations. |
| Keywords: | gradient neural network(GNN) linear matrix equation lyapunov stability theory global exponential convergence asymptotical convergence |
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