带有时滞的马尔可夫跳线性系统最优滤波问题-数学专业论文.docxVIP

摘要 摘要 万方数据 万方数据 摘 要 近年来, 时滞系统的研究取得了一系列的重要成果, 得到了飞速的发展. 这些成 果为带有时滞的马尔可夫跳线性系统的最优滤波器的设计开辟了新的领域. 但是, 以 往的处理马尔可夫跳线线性系统时滞问题的方法还未曾有过用递推的思想来处理马 尔可夫跳线线性系统的时滞项. 本文采用了递推法来处理时滞项, 把将带有时滞的马 尔可夫跳线线性系统转换为没有时滞的马尔可夫跳线性系统, 给出了不含时滞的马尔 可夫跳线性系统的最优滤波问题. 然后设计了最优滤波器, 用估计误差方差的方法验 证了最优滤波器设计的合理性. 与以往的方法相比该方法更简单易懂, 过程虽看似很 复杂但是结果却很有规律, 运用起来很方便. 本文主要对以下几个方面的问题进行了研究和分析: (1) 针对一类观测变量中含有确定时滞的离散马尔可夫跳线性系统进行了研究, 用数学递推的方法转化为没有时滞项的马尔可夫跳线性系统. (2) 研究没有时滞项的最优滤波问题, 给出最优滤波器的设计, 并得到了带有时 滞的马尔可夫跳线性系统的最优滤波器的系数矩阵的形式. (3)给出状态变量估计值, 并运用估计误差方差方法验证了最优滤波器设计的合 理性. 关键词: 马尔可夫跳线性系统; 时滞; 滤波器; 代数黎卡提方程. i Abstract Abstract Abstract In the recent years, time-delay systems have a series of important results. It has been developed rapidly. The design of optimal ?lter of Markov jumper linear systems with time-delay opens up a new areas . However, in order to processing with the delay jumper method of Markov linear systems someone have already build a large new sequence information , there had not been used delay idea to handle recursive Markov linear systems jumper items.This paper uses a recursive method to deal with time delays , so the jumper Markov linear systems with time delay is converted the Markov jumper system with no time delay , Then the optimal ?lter of the system with no time delay is designed, Compared with the conventional method, the method used in the paper is more straightforward. Although the process of computing seems complicated ,the result is very regular, it is very easy to use . The main contents of this paper are summarized as follows : The optimal ?ltr problem of linear time delay the system with Markov jumps is disscused by a refund method of changing the sytem into one with no time delay. Using the optimal ?ltering problems which system does not have time-delay terms , and gives the form of the coe?cient matrix of Markov jumper systems with time-delay . Using estimated values of state variables are given and useing the estimation error variance to verify the rationality of the optimal ?lter design. Ke