【作者】 卢晓；

【导师】 张焕水； 王伟；

【作者基本信息】 大连理工大学 ， 控制理论与控制工程， 2008， 博士

【摘要】 线性估计问题是控制、通信、信号处理等领域一个重要的研究课题。20世纪60年代提出的Kalman滤波理论成为近几十年来估计和控制的主要研究工具,但是标准的Kalman滤波理论只能处理正常系统,而不适合时滞系统。时滞系统的估计和控制问题,由于实际的需要已引起人们广泛的关注,至今有些问题如含有时滞观测的线性系统的估计问题、输入带时滞的控制等问题还没有得到足够的研究。本论文将针对时滞观测的线性系统提出一种最优估计的新方法,即新息重组分析方法。其基本思想是将带有时滞的观测数据重新组合成为来自不同观测系统但无时滞的观测数据,然后对重组后的观测数据定义新息序列,由此提出全新的Kalman滤波公式,进而得到复杂的白噪声H_∞估计器、时滞鲁棒Kalman滤波器及时滞信息融合滤波。本文的主要工作如下:研究了离散情况下时滞系统的Kalman滤波问题。引入离散系统的新息重组分析方法,分析了含有即时观测和单时滞观测的情况,得到了优化滤波器,进而推导出非常复杂的线性离散系统多时滞情况下的新息重组分析方法,给出此时的最优滤波器以及计算的流程图。该方法一个重要的优点是计算量比传统的系统增广方法大大减少了,文中给出了两种方法计算量上的比较,并通过两个例子进行了验证,根据一个仿真例子验证了所给方法的有效性。并将离散单时滞系统的结果应用到鲁棒和时滞信息融合滤波问题上,给出了一个时滞系统的鲁棒Kalman滤波器和时滞信息融合滤波器。研究了连续情况下时滞系统的Kalman滤波问题。提出了连续时滞系统新息重组分析方法,对含有即时观测和单时滞观测的情况进行了深入地研究,进而将其推广到更一般的多时滞观测的情况,给出了含有即时观测和时滞观测情况下的最优滤波器,并利用实例和流程图直观得体现了算法的实现过程,方法中没有采用传统的偏微分方法,得到了显式解。提出的新息重组分析方法可以用来处理很多复杂的问题,其中H_∞白噪声估计问题就是一个重要的应用。引入Krein空间,借助新息重组分析方法、射影定理,研究了线性系统（包括离散和连续情况）的白噪声估计问题,给出了H_∞估计器（主要是滤波器和固定时滞平滑器）及其存在的充要条件。揭示出H_∞白噪声滤波问题实际上等价于Krein空间内的H₂白噪声滤波问题,而H_∞白噪声固定时滞平滑问题实际上等价于Krein空间内含即时观测和单时滞观测的系统的H₂白噪声估计问题。本课题具有非常重要的理论价值和实际意义。更多还原

【Abstract】 Linear Estimation is a key research topic in many fields such as control, communications, signal processing, and so on. In the 1960’s, Kalman filtering was presented and has been a major tool of state estimation and control since then. However, the standard Kalman filtering can be only applicable to the normal systems without delays not to the delayed systems. Much interest has been attached to the case of time delays for the actual requirements. Some problems such as estimation for linear systems with delayed measurements and control for systems with input delay haven’t been studied well up to the present. In this paper, we are concerned with the optimal estimation problem for linear systems systems with delayed measurements, and a new optimal approach, re-organization of innovation analysis, is then proposed. The main idea is to re-organize the delayed measurements into delay-free measurements from different systems, and the associated innovation sequence is given in according to the re-organized measurements, Kalman filtering formulations based on the new approach are thus given. With the new technique, the more complicated H_∞white noise estimator, robust time-delayed Kalman filter, and time-delayed information fusion filter are then given. The paper mainly includes the following parts:Kalman filtering for linear discrete-time systems with delayed measurements. Reorganization of innovation analysis for discrete-time systems is introduced, and the case of systems with instantaneous measurement and delayed measurements is studied, the optimal filters are then given. Furthermore, the more complicated technique, re-organization of innovation analysis, is derived for discrete-time systems with multiple delayed measurements, and optimal filters and the flow chart are also given in the paper. Such an approach is much more computationally attractive which is a major advantage over the traditional system augmentation, and the comparison of the computation costs between the proposed re-organization of innovation analysis and the traditional augmentation method is also given, and two examples have been given to show this point. A numerical example is given to show the efficiency of the proposed approach. The proposed approach is further extended to the robust Kalman filtering for discrete-time systems with single delayed measurement and the time-delayed information fusion filtering problem, then the robust Kalman filter and the time-delayed information fusion filter are given.Kalman filtering for linear continuous-time systems with delayed measurements. Reorganization of innovation analysis for continuous-time systems is presented, the case of systems with instantaneous measurement and delayed measurements is studied well, and the proposed approach is extended to the case of continuous-time systems with multiple delayed measurements, and optimal filters are given. Two numerical examples and the flowchart for the computation are given to show the process of the computation. Explicit solutions to the problem are given without resorting to traditional partial differential equations.Re-organization of innovation analysis can be used to deal with many difficult problems, one of which is H_∞white noise estimation. In the paper, Krein space is introduced, and the H_∞white noise estimation for linear systems （including both discrete-time case and continuous-time case） is considered with the help of re-organization of innovation analysis and projection formulation in Krein space, thus the estimators （mainly filters and fixed-lag smoothers） and the associated sufficient and essential conditions are given. It is also shown that the white noise H_∞white noise filtering is equivalent to the H₂ white noise filtering in Krein space, and the H_∞white noise fixed-lag smoothing is in fact equivalent to an H₂ estimation problem for measurement delayed system in Krein space. The problem is much valuable both in theory and in practice.更多还原