面向智能计算的神经网络稳定性集值映射方法研究

项目名称： 面向智能计算的神经网络稳定性集值映射方法研究

项目编号： No.61472093

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 自动化技术、计算机技术

项目作者： 刘自鑫

作者单位： 贵州财经大学

项目金额： 84万元

中文摘要： 为解决博弈论中Nash平衡点的神经网络求解技术问题，实现计算机网络资源最优分配的智能计算，弥补现有神经网络稳定性判据互通性差的缺陷，项目主要从集值映射观点出发，研究智能计算神经网络的多稳定性问题，探索多种神经网络模型的统一研究模式，建立新的存在性和稳定性判据。对多稳定性问题，利用非线性分析中的集值映射理论，将多稳定神经网络理解为一个特殊的集值映射，研究神经元激活函数发生和不发生改变两种情形下，平衡点及周期解的存在性及多稳定性判据；对探寻神经网络统一研究模式问题，在分析各种神经网络模型共同本质特征基础之上，探索利用微分包含式来建立多种神经网络模型的统一研究模式，并利用集值映射理论、不动点理论等非线性分析工具，研究微分包含统一模式下，神经元激活函数发生和不发生改变时，多种神经网络平衡点和周期解的通有存在性和通有稳定性。项目最后将应用上述理论成果，实现博弈理论和网络资分配问题平衡点的智能计算。

中文关键词： 神经网络；智能计算；集值映射；微分包含；网络资源管理

英文摘要： In order to solve the intelligent computing problem of game theory and network resources allocation by neural network, and overcome the poor interoperability of the existing neural network's stable criteria,the main aim of this project is to establish some new existence and stability criteria for intelligent computing multistable neural networks from set-valued mapping piont of view, and explore a new unifed research way to research various tpyes of neural network models. For the multistable problem, from set-valued mapping piont of view, multistable neural network can be look as a special set-valued mapping. In this case, this project palns to research the existence and stability problems of equilibrium point and periodic solution when the neural activation function changes or not changes. Aditional, In order to find a way to research various tpyes of neural network models in an unifed framework. By analyzing the common essential characteristics of these different models, this project attempts to translate these various tpyes of neural network models into uniform differential inclusive models. By ultilizing set-valued mapping theory, fixed piont theory, and all kinds of nonlinear analysis tool, this project attempts to further establish some new generic existence and stability criteria when the activate function changes or not changes.As an application, this project will further consider to use the obtained theoretical results to realize the intelligent computation of game theory and network resources allocation.

英文关键词： Neural network;Intelligent computing;Set-valued mapping;Differential inclusion;Network resource management