脉冲随机系统的稳定性、随机镇定及其在神经网络中的应用研究

项目名称： 脉冲随机系统的稳定性、随机镇定及其在神经网络中的应用研究

项目编号： No.11301004

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 程培

作者单位： 安徽大学

项目金额： 22万元

中文摘要： 鉴于随机噪声可以用来镇定不稳定的微分系统或使给定微分系统的解由指数增长变成最多多项式增长,本课题主要研究一般形式的线性和非线性脉冲随机系统的稳定性以及随机噪声镇定和状态反馈镇定问题。其中，对于线性系统，基于Lyapunov 稳定性理论，利用遍历理论和算子半群理论，建立其a.s.指数稳定和多项式增长的判据；对一般的非线性系统，在系统系数满足单边线性增长或多项式增长条件下，利用Ito 公式、Doob 鞅指数不等式、B-D-G不等式及Borel-Cantelli 引理等随机分析技巧建立其a.s.指数稳定和多项式增长的一般定理,并给出系统基于LMIs 形式的稳定性充分条件；在稳定性研究的基础上进而给出系统随机噪声镇定和状态反馈的控制策略。最后将理论结果应用于随机网络的噪声镇定研究中。本课题的研究将丰富混杂随机系统控制理论，为人们更深入地认识随机噪声对自然系统和工程系统的影响规律提供理论分析方法。

中文关键词： 脉冲随机系统；指数稳定；噪声镇定；脉冲镇定；神经网络

英文摘要： Noise can be used to stabilize a given unstable system or to make a given system whose solutions grow exponentially become a new system whose solutions will grow at most polynomially.This project mainly focuses on the stability, stochastic noise stabilization, and state feedback stabilization of general linear and nonlinear impulsive stochastic systems. In detail, for linear systems, based on the Lyapunov stability theory, we will establish some criteria on the almost sure exponential stability and polynomially growth by using the ergodic theory and semigroup theory.And for the general nonlinear systems, by utilizing the Ito formula, Doob martingale exponential inequalities,Burkholder-Davis-Gundy inequality, and the Borel-Cantelli Lemma, the general theorem on the almost sure exponential stability and polynomially growth will be proposed, and some sufficient conditions on the stability will also be given in terms of LMIs. Furthermore, based on the stability results obtained,the exact method how to design a noise control and state-feedback control to stabilize a given linear or nonlinear impulsive stochastic system will be discussed. At last, their applications to neural networks will also be proposed.The researches of this project will rich the stability theory of hybrid stochastic systems, and it may be provide

英文关键词： Impulsive stochastic systems；Exponential stability；Noise stabilization；Impulsive stabilization；Neural network