时滞系统线性二次微分对策估计与控制

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 theoretic tracking control and so on. Therefore, the topic is significant both in the theory and the application.

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。

该项目考虑了时滞系统控制理论中的估计问题，主要研究了微分对策估计、H无穷估计、风险灵敏估计、最优序列估计和信息估计等问题。应用线性二次微分对策、变分法、不定空间及新息分析等理论，设计出了时滞系统的各种估计器，提出有效地处理线性时滞系统估计问题的切实可行的方法，给出时滞系统估计器的解析解及存在的条件，同时对估计器的稳定性与收敛性进行分析，得到估计器的收敛条件；阐明时滞线性系统微分对策估计、H无穷估计、风险灵敏估计的内在联系；揭示时滞系统与无时滞系统的估计器设计的本质区别，因此本项目的研究有重要的理论和应用意义。