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Mathematics
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Discrete Event Dynamic Systems and Applications
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Discrete Event Dynamic Systems and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 31 December 2025 | Viewed by 4812

Special Issue Editors

Prof. Dr. Gaiyun Liu

E-Mail Website
Guest Editor
GREAH—EA3220 (Groupe de Recherche en Electrotechnique et Automatique du Havre), Université Le Havre Normandie, 76600 Le Havre, France
Interests: discrete event system; supervisory control; formal method; security analysis
Prof. Dr. Dimitri Lefebvre

E-Mail Website
Guest Editor
GREAH—EA3220 (Groupe de Recherche en Electrotechnique et Automatique du Havre), Université Le Havre Normandie, 76600 Le Havre, France
Interests: discrete event systems; formal methods; artificial intelligence; cyber–physical systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent years, cyber–physical systems have been widely used in the fields of intelligent manufacturing, power systems, logistics management, healthcare systems, intelligent transportation systems, robotics and computer communication networks. At a certain technical abstraction level, these systems have the characteristics of networked discrete event dynamic systems (DEDSs). Under the formal framework, studying cyber–physical systems from the perspective of networked DEDSs is the key means to solve their technical application problems. Such systems are usually constructed and operated in a distributed mode with communication networks. On one hand, the use of communication networks enhances the capability and intelligence of DEDS information processing; on the other hand, it increases the risk of the system facing external cyber attacks.

The aim of this Special Issue is to collect the latest advances in modeling (such as automata, timed automata, probabilistic automata, Petri nets, Markov models, Queues, max-plus algebras), security analysis, control and optimization, performance evaluation, and applications of DEDSs. Interested authors are welcome to share their academic results and practical experiences to address these challenging issues in the field.

Prof. Dr. Gaiyun Liu
Prof. Dr. Dimitri Lefebvre
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • discrete event dynamic system
  • formal method
  • property verification
  • networked control system
  • cyber security
  • system control
  • optimization and scheduling
  • distributed system
  • system reconfiguration
  • stochastic process and uncertainty
  • timing aspects in DEDS and hybrid systems
  • cyber–physical system
  • artificial intelligence in discrete event dynamic system
  • applications of discrete event dynamic system

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Published Papers (5 papers)

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19 pages, 725 KiB  
Article
Critical Observability of Stochastic Discrete Event Systems Under Intermittent Loss of Observations
by Xuya Cong, Haoming Zhu, Wending Cui, Guoyin Zhao and Zhenhua Yu
Mathematics 2025, 13(9), 1426; https://doi.org/10.3390/math13091426 - 26 Apr 2025
Viewed by 223
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Discrete Event Dynamic Systems and Applications)
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15 pages, 564 KiB  
Article
Calculation and Analysis of Petri Net Reachability Graphs by a Think-Globally-Act-Locally Method
by Chengzong Li, Fubao Jin, Yufeng Chen, Zhiwu Li, Murat Uzam and Huimin Ma
Mathematics 2025, 13(5), 793; https://doi.org/10.3390/math13050793 - 27 Feb 2025
Viewed by 545
Abstract
A think-globally-act-locally (TGAL) technique is proven to be an effective method to address the state explosion issue for complex discrete event systems modeled with Petri nets. This paper introduces a TGAL-based method for computing and analyzing the reachability graph (RG) of Petri net [...] Read more.
A think-globally-act-locally (TGAL) technique is proven to be an effective method to address the state explosion issue for complex discrete event systems modeled with Petri nets. This paper introduces a TGAL-based method for computing and analyzing the reachability graph (RG) of Petri net models. Given a net system, the TGAL technique strategically introduces a global idle place (GIP) to iteratively generate its RG by updating the token count. At each step, the reachable markings (RMs) and legal markings (LMs) obtained by the previous iterations are considered to calculate the corresponding states of the current step. According to the enforced control requirement, a system state is required to be computed and classified only once during an iterative process. This method only calculates the necessary number of RMs and reduces computational redundancy, which minimizes the computational cost. Four typical Petri net models from existing studies are employed to demonstrate the method. Full article
(This article belongs to the Special Issue Discrete Event Dynamic Systems and Applications)
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24 pages, 838 KiB  
Article
On Deadlock Analysis and Characterization of Labeled Petri Nets with Undistinguishable and Unobservable Transitions
by Amal Zaghdoud and Zhiwu Li
Mathematics 2024, 12(22), 3523; https://doi.org/10.3390/math12223523 - 12 Nov 2024
Viewed by 1021
Abstract
This work addresses the analysis and characterization of deadlocks in discrete-event systems modeled by labeled Petri nets (LPNs) with undistinguishable and unobservable transitions. To provide a solution for the notorious problem, it is essential to present an effective characterization in such a way [...] Read more.
This work addresses the analysis and characterization of deadlocks in discrete-event systems modeled by labeled Petri nets (LPNs) with undistinguishable and unobservable transitions. To provide a solution for the notorious problem, it is essential to present an effective characterization in such a way that deadlock control and synthesis are technically and methodologically possible. To this end, we introduce the notion of dangerous implicit vectors (DIVs), which implicitly threaten the system deadlock-freedom. The set of dead markings is divided into two subsets: dead basis markings (DBMs) and dangerous implicit markings (DIMs). An algorithm is designed to compute the sets of DIVs and DIMs at a given basis state of a system. Moreover, by virtue of linear algebraic equations, we formulate sufficient conditions for identifying the existence of blocking markings in an LPN. Finally, an algorithm is developed to construct an observed graph that is a compendious presentation of the reachability graph of a net system, with respect to the existence of dead reaches. At the end of this paper, experiment results that illustrate the correctness and effectiveness of the reported solution are presented. Full article
(This article belongs to the Special Issue Discrete Event Dynamic Systems and Applications)
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21 pages, 1042 KiB  
Article
Detection of Cyber-Attacks in a Discrete Event System Based on Deep Learning
by Sichen Ding, Gaiyun Liu, Li Yin, Jianzhou Wang and Zhiwu Li
Mathematics 2024, 12(17), 2635; https://doi.org/10.3390/math12172635 - 25 Aug 2024
Cited by 2 | Viewed by 1136
Abstract
This paper addresses the problem of cyber-attack detection in a discrete event system by proposing a novel model. The model utilizes graph convolutional networks to extract spatial features from event sequences. Subsequently, it employs gated recurrent units to re-extract spatio-temporal features from these [...] Read more.
This paper addresses the problem of cyber-attack detection in a discrete event system by proposing a novel model. The model utilizes graph convolutional networks to extract spatial features from event sequences. Subsequently, it employs gated recurrent units to re-extract spatio-temporal features from these spatial features. The obtained spatio-temporal features are then fed into an attention model. This approach enables the model to learn the importance of different event sequences, ensuring that it is sufficiently general for identifying cyber-attacks, obviating the need to specify attack types. Compared with traditional methods that rely on synchronous product computations to synthesize diagnosers, our deep learning-based model circumvents state explosion problems. Our method facilitates real-time and efficient cyber-attack detection, eliminating the necessity to specifically identify system states or distinguish attack types, thereby significantly simplifying the diagnostic process. Additionally, we set an adjustable probability threshold to determine whether an event sequence has been compromised, allowing for customization to meet diverse requirements. Experimental results demonstrate that the proposed method performs well in cyber-attack detection, achieving over 99.9% accuracy at a 1% threshold and a weighted F1-score of 0.8126, validating its superior performance. Full article
(This article belongs to the Special Issue Discrete Event Dynamic Systems and Applications)
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20 pages, 3401 KiB  
Article
Wafer Delay Minimization in Scheduling Single-Arm Cluster Tools with Two-Space Process Modules
by Chengyu Zou, Siwei Zhang, Shan Zeng, Lei Gu and Jie Li
Mathematics 2024, 12(12), 1783; https://doi.org/10.3390/math12121783 - 7 Jun 2024
Viewed by 876
Abstract
In semiconductor manufacturing, multi-space process modules (PMs) are adopted in some cluster tools for wafer processing. With multi-space PMs, a PM can have multiple wafers concurrently. Also, the internal chamber in a PM should rotate to make the robot able to load/unload a [...] Read more.
In semiconductor manufacturing, multi-space process modules (PMs) are adopted in some cluster tools for wafer processing. With multi-space PMs, a PM can have multiple wafers concurrently. Also, the internal chamber in a PM should rotate to make the robot able to load/unload a wafer into/from a space in the PM. This means that the wafer staying time in PMs is affected by both the rotation operations of the internal chambers of PMs and the robot tasks. Thus, minimizing the wafer delay time is quite challenging. In this work, for cluster tools with single-arm robots and two-space PMs, efforts are made for wafer delay minimization in scheduling the tools. Specifically, a two-wafer backward strategy is presented to operate the tools in a steady state. Then, the workloads of each processing step and the robot are analyzed. Further, to find optimal schedules with the objective of minimizing the total wafer delay time, efficient algorithms are established. Finally, case studies show that the wafer delay time at some steps can be totally eliminated by the proposed method. In the meantime, in all cases, the proposed method can work well in reducing the total wafer delay time at all steps. Full article
(This article belongs to the Special Issue Discrete Event Dynamic Systems and Applications)
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