文章基本信息

标题：Compositional Synthesis of Finite Abstractions for Continuous-Space Stochastic Control Systems: A Small-Gain Approach ⁎
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作者：Abolfazl Lavaei ; Sadegh Soudjani ; Majid Zamani 等
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2018
卷号：51
期号：16
页码：265-270
DOI：10.1016/j.ifacol.2018.08.045
语种：English
出版社：Elsevier
摘要：AbstractThis paper is concerned with a compositional approach for constructing finite abstractions (a.k.a. finite Markov decision processes) of interconnected discrete-time stochastic control systems. The proposed framework is based on a notion of so-calledstochastic simulation functionenabling us to use an abstract system as a substitution of the original one in the controller design process with guaranteed error bounds. In the first part of the paper, we derive sufficient small-gain type conditions for the compositional quantification of the distance in probability between the interconnection of stochastic control subsystems and that of their (finite or infinite) abstractions. In the second part of the paper, we construct finite abstractions together with their corresponding stochastic simulation functions for the class of linear stochastic control systems. We apply our results to the temperature regulation in a circular building by constructing compositionally a finite abstraction of a network containing 1000 rooms. We use the constructed finite abstractions as substitutes to synthesize policies compositionally regulating the temperature in each room for a bounded time horizon.
关键词：KeywordsInterconnected Stochastic Control SystemsCompositionalityFinite AbstractionsFinite Markov Decision ProcessesSmall-Gain ConditionsFormal Synthesis