系统首达控制域时间的离散分布特性  

The Discrete Distributing Characteristic of the Initial Time for a System to Reach a Control Region

作　　者：刘力维[1] 陆中胜[1] 侯传志[1] 

机构地区：[1]南京理工大学理学院,江苏南京210094

出　　处：《数学的实践与认识》2011年第6期133-139,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(60874118)

摘　　要：文章研究被控系统首达控制域时间的概率分布问题.通过对被控量的离散化处理并借助于近代发展起来的Phase-Type分布理论,求出了首达控制域时间的各阶条件矩,并将其转化为求解代数方程组.然后,求出了首达时间的条件L-S变换和条件分布.最后,说明了系统状态转移矩阵及PH分布的确定问题.整篇文章解决了首达控制域时间分布的描述与求解问题.The problem of the probability distribution of the time for a controlled system first to reach a control region is studied. By the disposal of discretization to the controlled object and the theory of Phase-Type distribution developed in the modern times, the paper gains the conditional moments of the initial time for a system to get the control region and, then, changes them into solving algebraic equations. After that, the conditional L-S transformation and the conditional distribution of the initial time are deduced. Finally, the paper explains the estimation problems to the state transition matrix of the system and PH distribution. The whole paper settles the description of the distribution of the initial time and the corresponding solving methods.

关 键 词：控制论 随机过程 PH分布 概率分布 

分 类 号：O211.3[理学—概率论与数理统计]