时滞系统线性二次微分对策估计与控制

项目名称： 时滞系统线性二次微分对策估计与控制

项目编号： No.61273124

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 赵洪国

作者单位： 泰山学院

项目金额： 76万元

中文摘要： 本项目应用线性二次微分对策、变分法及观测重组等理论，研究线性时滞系统估计与控制中的最大最小问题（微分对策估计与控制问题）。微分对策理论是研究估计与控制问题的一种重要的数学工具，然而由于系统中存在时滞，微分对策理论不能直接应用于时滞系统解决估计与控制问题，目前相关的研究成果尚不多见。本项目旨在提出有效地处理时滞系统线性二次微分对策估计与控制的切实可行的方法，给出时滞系统微分对策估计器与控制器的解析解及其存在的条件，同时对微分对策控制器和估计器的稳定性与收敛性进行详细分析，得到控制器与估计器的收敛条件；阐明时滞线性系统微分对策控制与微分对策估计的内在联系；揭示时滞系统与无时滞系统的微分对策控制器与微分对策估计器设计的本质区别。本项目的研究将为解决时滞系统中其它的疑难问题，如微分对策跟踪控制等问题提供新思路，对揭示时滞系统的内在规律具有重要的意义。

中文关键词： 线性时滞系统；微分对策；重组新息；；

英文摘要： The problems of max-min estimation and control (differential game theoretic estimation and control) for linear time-delay systems are investigated based on linear quadratic differential game,calculus of variations and reorganized observation theory.The differential game theory is an important class of mathematical tool for estimation and control for linear delay-free systems. However, it can not be directly applied to solve estimation and control problem for time-delay systems because of time-delays in systems. Hence, there exists few related result.The purposes of the project are multiple and include to propose a novel approaches to deal with the linear quadratic differential game theoretic estimation and control for time-delay systems, study further the steady-state differential game theoretic estimation and control as well as convergence conditions,give the explicit analytic expressions of the differential game theoretic estimation and control as well as the necessary and sufficient conditions of existence, provide the deep link between the differential game theoretic estimation and control, explain essential differences between the differential game theoretic estimation and control for time-delay systems and that for delay-free systems. The new approach proposed will be helpful to solve differential game the

英文关键词： Linear time delay systems；differential game；reorganized innovation；；