State Estimation and Detectability of Probabilistic Discrete Event Systems.
State Estimation and Detectability of Probabilistic Discrete Event Systems.
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DOI：
10.1016/j.automatica.2008.05.025
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发表时间：
2008-12-01
期刊：
影响因子：
6.4
通讯作者：
Chen, Xinguang
中科院分区：
文献类型：
--
作者：
Shu, Shaolong;Lin, Feng;Ying, Hao;Chen, Xinguang
概率离散事件系统（PDES）是一种非确定性离散事件系统，其中非确定性转移的概率被指定。PDES的状态估计问题比非概率离散事件系统的状态估计问题困难得多。在我们以前的论文中，我们研究了非概率离散事件系统的状态估计问题。我们定义了四种类型的可检测性，并推导出检查这些可检测性的充分必要条件。在本文中，我们将我们的研究扩展到考虑概率的PDES状态估计问题。在我们的方法中的第一步是将一个给定的PDES转换成一个不确定的离散事件系统，并找到检查概率可检测性的充分条件。接下来，为了找到检查概率可检测性的充分必要条件，我们研究了PDES中事件序列的“收敛性”。一个事件序列是收敛的，如果沿着这个序列，系统越来越确定地处于一个特定的状态。我们推导出收敛的条件，从而为检测。我们专注于完全事件观测和无状态观测的系统。为了更好地介绍，理论的发展，说明了一个简化的例子肾炎诊断。
A probabilistic discrete event system (PDES) is a nondeterministic discrete event system where the probabilities of nondeterministic transitions are specified. State estimation problems of PDES are more difficult than those of non-probabilistic discrete event systems. In our previous papers, we investigated state estimation problems for non-probabilistic discrete event systems. We defined four types of detectabilities and derived necessary and sufficient conditions for checking these detectabilities. In this paper, we extend our study to state estimation problems for PDES by considering the probabilities. The first step in our approach is to convert a given PDES into a nondeterministic discrete event system and find sufficient conditions for checking probabilistic detectabilities. Next, to find necessary and sufficient conditions for checking probabilistic detectabilities, we investigate the “convergence” of event sequences in PDES. An event sequence is convergent if along this sequence, it is more and more certain that the system is in a particular state. We derive conditions for convergence and hence for detectabilities. We focus on systems with complete event observation and no state observation. For better presentation, the theoretical development is illustrated by a simplified example of nephritis diagnosis.
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