Markov Set-Chains as Abstractions of Stochastic Hybrid Systems
Markov Set-Chains as Abstractions of Stochastic Hybrid Systems
复制标题
作为随机混合系统抽象的马尔可夫集链
DOI：
10.1007/978-3-540-78929-1_1
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
S. Sastry
中科院分区：
文献类型：
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作者：
A. Abate;A. D’innocenzo;M. D. Benedetto;S. Sastry
本研究的目的是介绍一种适用于一般动力系统的抽象过程，即离散时间随机混合系统（dt-SHS）。该过程分两步将原始dt-SHS抽象成一个马尔可夫集链（MSC）。首先，根据可控制参数将混合状态空间划分为不重叠的域，并根据dt-SHS的动力学特性计算这些域的转移概率，得到马尔可夫链。其次，导出了依赖于上述参数的抽象的显式误差界限，并将其与计算的MC转移概率相关联，从而得到了一个MSC；我们表明，可以通过调整可控参数任意增加抽象的准确性，尽管在增加的基数的MSC。借助MSC文献中的一些结果，可以分析原始dt-SHS的动力学。在本工作中，在抽象框架内评估了dt-SHS动力学的渐近行为。
The objective of this study is to introduce an abstraction procedure that applies to a general class of dynamical systems, that is to discrete-time stochastic hybrid systems (dt-SHS). The procedure abstracts the original dt-SHS into a Markov set-chain (MSC) in two steps. First, a Markov chain (MC) is obtained by partitioning the hybrid state space, according to a controllable parameter, into non-overlapping domains and computing transition probabilities for these domains according to the dynamics of the dt-SHS. Second, explicit error bounds for the abstraction that depend on the above parameter are derived, and are associated to the computed transition probabilities of the MC, thus obtaining a MSC. We show that one can arbitrarily increase the accuracy of the abstraction by tuning the controllable parameter, albeit at an increase of the cardinality of the MSC. Resorting to a number of results from the MSC literature allows the analysis of the dynamics of the original dt-SHS. In the present work, the asymptotic behavior of the dt-SHS dynamics is assessed within the abstracted framework.