Critical Observability of Stochastic Discrete Event Systems Under Intermittent Loss of Observations

Xuya Cong, Haoming Zhu (), Wending Cui, Guoyin Zhao and Zhenhua Yu
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Xuya Cong: College of Artificial Intelligence and Computer Science, Xi’an University of Science and Technology, Xi’an 710054, China
Haoming Zhu: College of Safety Science and Engineering, Xi’an University of Science and Technology, Xi’an 710054, China
Wending Cui: College of Artificial Intelligence and Computer Science, Xi’an University of Science and Technology, Xi’an 710054, China
Guoyin Zhao: College of Artificial Intelligence and Computer Science, Xi’an University of Science and Technology, Xi’an 710054, China
Zhenhua Yu: College of Artificial Intelligence and Computer Science, Xi’an University of Science and Technology, Xi’an 710054, China

Mathematics, 2025, vol. 13, issue 9, 1-19

Abstract: A system is said to be critically observable if the operator can always determine whether the current state belongs to a set of critical states. Due to the communication failures, systems may suffer from intermittent loss of observations, which makes the system not critically observable. In this sense, to characterize critical observability in a quantitative way, this paper extends the notion of critical observability to stochastic discrete event systems modeled as partially observable probabilistic finite automata. Two new notions, called step-based almost critical observability and almost critical observability are proposed, which describe a measure of critical observability for a given system against intermittent loss of observations. We introduce a new language operation to obtain a probabilistic finite automaton describing the behavior of the plant system under intermittent loss of observations. Based on this structure, we also present verification methodologies to check the aforementioned two notions and analyze the complexity. Finally, the results are applied to a raw coal processing system, which shows the effectiveness of the proposed methods.

Keywords: critical observability; discrete event system; cyber-physical system; stochastic process; Markov chain (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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