最近点投影型反馈神经网络的临界分析  

Critical Analysis of Recurrent Neural Networks with Nearest Point Projection

作　　者：乔琛[1] 徐宗本[1] 

机构地区：[1]西安交通大学理学院信息科学系,西安710049

出　　处：《工程数学学报》2009年第1期1-7,共7页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10371097;70531030)

摘　　要：基于Lyapunov泛函方法和矩阵理论,本文研究一类被广泛应用的反馈神经网络―最近点投影型反馈神经网络的临界全局动力学性态,当网络具有非线性不扩张性质时,在临界条件下得到该类网络全局收敛性和渐近稳定性。所获结果改进了已知的有关该类网络临界分析的代表性结论(当连接矩阵拟对称时网络具有收敛性)。数值试验表明结果的正确性和有效性。By using the Lyapunov functional method and matrix theory, the critical dynamics behavior of recurrent neural networks with nearest point projection has been investigated. It is shown that such networks are globally convergent and asymptotically stable when the networks are nonlinear non-dilatation. The established results improve the typical convergent conclusions, e.g., the networks are convergent when the connection matrices are quasi-symmetric. One example shows the practical feasibility of the obtained critical results.

关 键 词：反馈神经网络 临界分析 收敛性 渐近稳定性 最近点投影 

分 类 号：O175.13[理学—数学]