Deadlocks should be eliminated in highly automated manufacturing systems since their occurrence implies the stoppage of the whole or partial system operation. Over the past decades, Petri nets are increasingly becoming one of the most popular and full-fledged mathematical tools to deal with deadlock problems due to their inherent characteristics. In a Petri net formalism, liveness is an important property of system safeness, which implies the absence of global and local deadlock situations in an automated manufacturing system. The liveness assessment can be performed by verifying the satisfiability of certain predicates on siphons, a well-known structural object in Petri nets. Therefore, siphons have received much attention to analyze and control systems modeled with Petri nets. Particularly, elementary siphon theory plays a key role in the development of structurally simple liveness-enforcing Petri net supervisors, leading to a variety of deadlock control approaches. This survey studies on the state-of-the-art elementary siphon theory of Petri nets including refined concepts of elementary siphons and their extended version, computation methods of siphons and elementary ones, controllability conditions, and their application to deadlock control. As a reference, this work attempts to provide a comprehensive and updated research survey on siphons, elementary siphons, and their applications to the deadlock resolution in Petri nets.

We propose a new deadlock prevention policy for an important class of resource allocation systems (RASs) that appear in the modeling of flexible manufacturing systems (FMSs). The model of this class in terms of generalized Petri nets is, namely, S⁴PR. On the basis of recent structural analysis results related to the elementary siphons in generalized Petri nets on one hand and an efficient deadlock avoidance policy proposed for the class of conjunctive/disjunctive (C/D) RASs on the other hand, we show how one can generate monitors to be added to a net system such that all its strict minimal siphons are max^′‐controlled and no insufficiently marked siphon is generated. Thereby, a new, simple, and more permissive liveness‐enforcing supervisor synthesis method for S⁴PR is established.

This work develops an iterative deadlock prevention method for a special class of Petri nets that can well model a variety of flexible manufacturing systems. A deadlock detection technique, called mixed integer programming (MIP), is used to find a strict minimal siphon (SMS) in a plant model without a complete enumeration of siphons. The policy consists of two phases. At the first phase, SMSs are obtained by MIP technique iteratively and monitors are added to the complementary sets of the SMSs. For the possible existence of new siphons generated after the first phase, we add monitors with their output arcs first pointed to source transitions at the second phase to avoid new siphons generating and then rearrange the output arcs step by step on condition that liveness is preserved. In addition, an algorithm is proposed to remove the redundant constraints of the MIP problem in this paper. The policy improves the behavioral permissiveness of the resulting net and greatly enhances the structural simplicity of the supervisor. Theoretical analysis and experimental results verify the effectiveness of the proposed method.

This paper investigates the problem of synthesizing network attacks against fault diagnosis in the context of discrete event systems (DESs). It is assumed that the sensor observations sent to the operator that monitors a system are tampered with by an active attacker. We first formulate the process of online fault diagnosis under attack. Then, from the attack viewpoint, we define a sensor network attacker as successful if it can degrade the fault diagnosis in the case of maintaining itself as undiscovered by the operator. To verify such an attacker, an information structure called a joint diagnoser (JD) is proposed, which describes all possible attacks in a given attack scenario. Based on the refined JD, i.e., stealthy joint diagnoser (SJD), we present an algorithmic procedure for synthesizing a successful attacker if it exists.

Accurate and rapid fault diagnosis is critical for active distribution networks characterized by growing structural complexity and diverse load profiles. This paper proposes a two-stage fault diagnosis framework that synergistically combines colored Petri nets (CPN) and fuzzy colored Petri nets (FCPN). In the first stage, a CPN fault zone search model employing a breadth-first search (BFS) strategy is developed to identify suspected faulty components by processing circuit breaker operation information and grid topology. In the second stage, an FCPN diagnosis model is constructed by extending hierarchical fuzzy Petri nets through color assignment to confidence tokens. A key feature of this model is a dedicated initial confidence assessment module that dynamically evaluates the reliability of protection and circuit breaker actions by synthesizing device self-check alarms and operational timing information, thereby overcoming the limitation of empirical, static confidence assignment in existing methods. The resulting initial confidence values are then propagated through a hierarchical confidence inference module to determine the fault likelihood of each suspected component. Comparative simulations across four fault scenarios demonstrate that the proposed method achieves higher diagnostic accuracy and stronger fault tolerance than state-of-the-art approaches, correctly identifying all faulty components even under degraded alarm conditions.