离散互馈神经网络并行稳定性控制  

Stability Control for Discrete Mutual Feedback Neural Network on Parallel Evolution

作　　者：王凯兴[1] 潘一山[1] 刘军朋[2] 

机构地区：[1]辽宁工程技术大学力学与工程学院,辽宁阜新123000 [2]辽宁工程技术大学理学院,辽宁阜新123000

出　　处：《控制工程》2013年第4期753-755,共3页Control Engineering of China

基　　金：国家重点基础研究发展规划(973计划)项目(2010CB226803);辽宁工程技术大学研究生科研立项项目(Y201200104)

摘　　要：证明了离散互馈Hopfield神经网络动力过程与线性方程组迭代求根过程具有同构关系,进而给出由线性方程组系数矩阵和增广矩阵生成离散互馈神经网络权值矩阵和阈值向量的方法。得出当线性方程组迭代收敛时,可依据方程组系数矩阵和增广矩阵构造出神经元连接权值矩阵和阈值向量使得离散互馈神经网络并行演化稳定,且对非对称有理数权值矩阵和阈值向量下离散互馈神经网络亦是稳定的。当线性方程组收敛点各分量绝对值大于1时网络的初始状态稳定于方程组收敛点的符号模式。最后给出算例验证此构造方法,对离散互馈神经网络并行演化稳定的控制作用,推广了离散互馈神经网络权值矩阵和阈值向量的形式,为更一般情况下离散互馈网络稳定性设计提供理论依据。The isomorphic relation between dynamic process of discrete mutual feedback Hopfield neural network and iterative process of linear equations finding roots is proved. The method of construction weight matrix and threshold vector of discrete mutual feedback Hopfield neural network by coefficient matrix and augmented matrix of linear equations is given. Conclusion that discrete mutual feed- back Hopfield neural network of parallel evolution is stability under the weight matrix and threshold vector given when linear equations convergence. Also stability for discrete mutual feedback neural network with asymmetric and rational number weight matrix and threshold vector. When the absolute value of the convergence point more than 1 the discrete mutual,feedback network have the stability state with the same symbol of the convergence point. Finally given cases verified the stability of discrete mutual feedback neural network on paral- lel evolution. The control method of this paper extended the traditional form of weight matrix and threshold vector providing theoretical basis for stability design of mutual feedback network in general case.

关 键 词：离散互馈神经网络 网络迭代 并行稳定 谱半径 不动点 

分 类 号：TP27[自动化与计算机技术—检测技术与自动化装置]