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Reachability and controllability analysis of probabilistic finite automata via a novel matrix method
Author(s) -
Zhang Zhipeng,
Chen Zengqiang,
Liu Zhongxin
Publication year - 2019
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.2160
Subject(s) - reachability , controllability , probabilistic logic , algebraic number , supervisory control , mathematics , computer science , tensor product , theoretical computer science , pure mathematics , control (management) , mathematical analysis , artificial intelligence , statistics
Probabilistic finite automata (PFAs) can exhibit a stochastic behavior, and its reachability and controllability is viewed as the first necessary step of supervisory control and stabilization. In this paper, the problems of reachability and controllability of PFAs are investigated under the framework of semi‐tensor product (STP) of matrices. First, a matrix‐based modeling approach to PFAs is proposed, and the dynamics of PFAs can be described as a discrete‐time bilinear expression. Meanwhile, the notions of reachability with a probability of one is formally defined, and F‐reachability with a probability of one is introduced. With the algebraic expression, necessary and sufficient conditions of such reachability are provided systematically. Second, F‐set controllability with a probability of one of PFAs is developed by introducing the F‐reachability with a probability of one, and the associated algebraic condition to verify such controllability are given. Finally, a simple example is illustrated to validate the proposed results.