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广义射影神经网络的指数稳定性 被引量：2

Exponential stability of a general projection neural network
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摘要 研究了一类广义射影神经网络,分析了它的稳定性和收敛性.当映射和非对称时,分别定义了恰当的能量函数,在适当的条件下证明了该网络的全局收敛性和指数稳定性.与已有结果相比,文中的稳定性条件并不需要映射的可微性及映射和的对称性.理论分析和数值实例表明所得结果适用于非单调问题,而且给定的条件易于验证.由于该网络可求解一大类优化和平衡问题,因此文中结论具有一定的理论价值和实际意义. A general projection neural network is considered, and its stability and convergence are analyzed. When the sum of the underlying mappings is asymmetric, global convergenee and exponential stability of the general projection neural network are strictly shown under mild conditions by defining the suitable energy functions, respectively. Compared with the existing results for this network, the given stability conditions do not require the differentiability of the mappings, and the symmetric of the sum of the mappings. Theoretical analysis and illustrative examples show that the obtained results can be applied to some non-monotone problems, and the given conditions can be easily checked. Since this network can be used to solve a broad class of optimization and equilibrium problems, the obtained results are significant in both theory and application.
作者 高兴宝 董宁
机构地区 陕西师范大学数学与信息科学学院
出处 《陕西师范大学学报（自然科学版）》 CAS CSCD 北大核心 2007年第1期5-8,共4页 Journal of Shaanxi Normal University：Natural Science Edition
基金 国家自然科学基金资助项目(60671063) 陕西省科学技术计划项目(2006A02)
关键词 广义射影神经网络 广义变分不等式 全局收敛性 指数稳定性 general projection neural network general variational inequality global convergence exponential stability
分类号 O221.2 [理学—运筹学与控制论] O175.13 [理学—基础数学]
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参考文献12

  • 1Xia Y S, Wang J. A general projection neural network for solving monotone variational inequalities and related optimization problems [J]. IEEE Transaction on Neural Networks, 2004, 15(2): 318-328.
  • 2Noor M A. Some developments in general variational inequalities [ J ]. Applied Mathematics and Computation, 2004, 152(1): 199-277.
  • 3He B S. Inexact implicit methods for monotone general variational inequalities [ J ]. Mathematical Programming(A), 1999, 86: 199-217.
  • 4Friesz T L, Bemstein D H, Mehta N J, et al. Day-to-day dynamic network disequilibria and idealized traveler information systems [J]. Operations Research, 1994, 42:1 120-1 136.
  • 5Xia Y S, Wang J. On the stability of globally projected dynamical systems [ J ]. Journal of Optimization Theory and Applications, 2000, 106(1): 129-150.
  • 6Gao X B. Exponential stability of globally projected dynamic systems [ J ]. IEEE Transaction on Neural Networks, 2003, 14(2): 426-431.
  • 7Xia Y S, Wang J. Global asymptotic and exponential stability of a dynamic neural system with asymmetric connection weights [J ]. IEEE Transaction on Automatic Control, 2001, 46(4): 635-638.
  • 8Xia Y S. A new neural network for solving linear and quadratic programming problems [J]. IEEE Transaction on Neural Networks, 1996, 7(6): 1544-1547.
  • 9Xia Y S, Wang J. A dual neural network for kinematic control of redundant robot manipulators [J]. IEEE Transaction on System, Man and Cybernetics, Part B,2001, 31(1): 147-154.
  • 10Ortega T M, Rheinboldt W C. Iterative Solution of Nonlinear Equation in Several Variables [ M]. New York: Academic Press, 1970.

二级参考文献1

共引文献2

同被引文献16

  • 1Harker P T, Pang J S. Finite-dimensional variationa- linequality and nonlinear complementarity problems: a survey oftheory, algorithms, and applications [J].Mathematical Programming, 1990, 48(1/3):161-220.
  • 2Gao Xingbao. A novel neural network for solving non- linear convex programming [J]. IEEE Transaction on Neural Networks, 2004, 15(3): 613-621.
  • 3Tank D W, Hopfield J J. Simple "neural" optimization networks: an A/D converter, signal decision circuit, and a linearprogramming circuit[J]. IEEE Transaction on Circuits and Systems, 1986, CAS-33(5):533-541.
  • 4He Bingshen, Yang Hai. A neural-network model for mon- otone linear asymmetric variational inequalities [J]. IEEE Transaction on Neural Networks, 2000, 11 ( 1 ) : 3-16.
  • 5Liang Xuebin, Si J. Global exponential stability of neu- ral networks with globally Lipschitz continuous activa- tions and its application to linear variational inequality problem[J]. IEEE Transaction on Neural Networks, 2001,12(2) : 349-359.
  • 6Xia Youshen, Wang Jin. On the stability of globally projected dynamical systems [J].Optimization Theory and Applications, 2000,106(1) :129-150.
  • 7Liu Qingshan, Cao Jinde, Xia Youshen.. A delayed neu- ral network for solving linear projection equations and its analysis [ J ]. IEEE Transaction on Neural Networks, 2005,16 (4) :834-843.
  • 8Cheng Long, Hou Zengguang, Tan Min. A delayed projectionneural network for solving linear variational inequalities[J]. IEEE Transaction on Neural Networks, 2009,20(6) :915-925.
  • 9Liu Zixin, Lu Shu, Zhong Shouming. A new delayed projection neural network for solvin.g linear variational inequalities and quadratic optimization problems[C]/// 2008 International Symposium on Computational Intel- ligence and Design. Los Alamitos:IEEE Computer So- ciety, 2008 ,1 : 211-214.
  • 10Cheng Long, Hou Zengguang, Tan Min. Solving linear variational inequalities by projection neural network with time-varying delays [J]. Physics Letters: A, 2009,373 : 1739-1743.

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陕西师范大学学报（自然科学版）
2007年 第1期

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