无限维线性随机脉冲系统的可控性及相关问题的研究

项目名称： 无限维线性随机脉冲系统的可控性及相关问题的研究

项目编号： No.11201215

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 申丽娟

作者单位： 同济大学

项目金额： 23万元

中文摘要： 随机可控性是随机控制理论的核心，随机脉冲系统的可控性由于在工程技术、神经网络、仿真智能等领域的广泛应用受到极大关注。利用随机微积分、系统分析工具等，我们将对无限维线性随机脉冲系统的可控性及相关问题进行分析与研究，重点研究以下几个问题：构造线性随机脉冲系统的伴随系统及拟倒向系统，建立拟倒向系统与线性随机脉冲系统之间的有效联系，研究线性随机脉冲系统的近似可控性和零可控性；利用分离原则和分析工具，研究一类线性随机脉冲系统的随机S-可控性；定义较弱的可检测性和可观性，利用观测Grammian泛函的性质及等价表示给出线性随机脉冲系统可检测性和可观性的Hautus判据等充要条件；所得结果不仅对线性随机脉冲系统可控性及相关问题做了深入研究，而且为解决实际问题如神经网络上的动力系统及Boolean网络的可控性提供了新思路与解决方法。

中文关键词： 可控性；线性系统；随机脉冲系统；；

英文摘要： The notion of stochastic controllability has played a central role throughout the stochastic control theory. The controllability of stochastic impulsive systems has received intensive attention because of its wide use in engineering, neural networks, intelligent simulation, etc. Using the theory such as stochastic calculus and system analysis methods, we will investigate the controllability and its related issues of infinite dimensional linear stochastic impulsive systems. The main problems to be studied in this program are as follows. First of all, we will construct the adjoint system and quasi-backward system of linear stochastic impulsive system, establish the effective relation of the quasi-backward system and the linear stochastic impulsive system and investigate the approximate and null controllability of the linear stochastic impulsive system. Second, with the use of separation principle and stochastic analysis approach, we will study the stochastic S-controllability of a class of linear stochastic impulsive system. And finally, we will define the weaker concepts of detectability and observability, and obtain some sufficient and necessary conditions such as Hautus-test by using the properties and equivalent expressions of observability Grammian functional. These results will not only make closer examinati

英文关键词： controllability；linear systems；stochastic impulsive systems；；