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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Xuya Cong & Haoming Zhu & Wending Cui & Guoyin Zhao & Zhenhua Yu, 2025. "Critical Observability of Stochastic Discrete Event Systems Under Intermittent Loss of Observations," Mathematics, MDPI, vol. 13(9), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1426-:d:1643354
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    References listed on IDEAS

    as
    1. Sian Zhou & Jiaxin Yu & Li Yin & Zhiwu Li, 2023. "Security Quantification for Discrete Event Systems Based on the Worth of States," Mathematics, MDPI, vol. 11(17), pages 1-17, August.
    2. Sichen Ding & Gaiyun Liu & Li Yin & Jianzhou Wang & Zhiwu Li, 2024. "Detection of Cyber-Attacks in a Discrete Event System Based on Deep Learning," Mathematics, MDPI, vol. 12(17), pages 1-21, August.
    3. Jie Zhang & Zhiwu Li, 2024. "Critical Observability Enforcement in Discrete Event Systems Using Differential Privacy," Mathematics, MDPI, vol. 12(23), pages 1-22, December.
    4. Abdeldjalil Labed & Ikram Saadaoui & Hanyu E & Mohammed A. El-Meligy & Zhiwu Li & Mohamed Sharaf, 2023. "Language Recovery in Discrete-Event Systems against Sensor Deception Attacks," Mathematics, MDPI, vol. 11(10), pages 1-15, May.
    Full references (including those not matched with items on IDEAS)

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