随机偏泛函微分系统的可控性

项目名称： 随机偏泛函微分系统的可控性

项目编号： No.10871077

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 金属学与金属工艺

项目作者： 刘斌

作者单位： 华中科技大学

项目金额： 24万元

中文摘要： 随机微分系统可控性是具有挑战性的研究领域，是联系随机微分系统和控制系统研究到实际应用问题的一个重要方面。本项目：建立了随机微分系统边界可控性的充分条件；给出了随机时滞发展系统最优控制存在与唯一性条件，并用于研究具动态边界条件的随机偏微分方程的最优控制问题；得到了具无限时滞偏泛函微分系统解的存在性与可控性条件；研究了具随机边界控制的HJB方程粘性解存在性；讨论了脉冲中立型随机发展系统mild解的存在性；研究了时滞随机发展系统解的局部存在性、惟一性和连续相依性；建立了时滞随机偏微分系统能量解是指数稳定的准则；得出了具无限时滞二阶非线性微分系统可控性的充分条件；进行了具马尔可夫调制中立型随机时滞微分系统和具Poission跳的随机年龄依赖人口模型的数值分析； 得到了关于一般可分距离空间上独立随机元系列的几乎处处中心极限定理；给出了随机时滞神经网络新的指数稳定条件。

中文关键词： 随机微分系统；可控性；偏泛函微分系统；发展系统

英文摘要： It is a challenging research area for the controllbility of the stochastic differential systems, and is an important aspect which connects stochastic differential systems and controll systems. The project: establish the sufficient conditions for the boundary controllability stochastic differential systems;give the conditions of existence and uniqueness of the optimal control for stochastic delay evolution equations, and to study an optimal control of stochastic partial differential equations with dynamical boundary conditions; obtain the conditions of controllability and existence for the partial fuanctional differential sysytems with infinite delay; study the existence of viscosity solution of HJB equation for stochastic boundary control problems; disscuss the the existence of mild solutions of a class of impulsive neutral stochastic evolution systems;study the local existence-uniqueness and continuation of solutions for delay stochastic evolution equations; establish the exponential stability criteria of delay stochastic functional differential equations; obtain the sufficient conditions the controllability of nonlinear second order neutral stochastic differential systems with infinite delay; investigate the numerical analysis for neutral stochastic delay differential equations with phase semi-Markovian switching and stochastic age-dependent population equations with Poisson jumpand; get the almost sure central limit theorems in separable metric space; give the new criteria on exponential stablity of stochastic delay neural networks.

英文关键词： stochastic differential systems ；Controllbility； Partial functional differential systems; Evolution systems