Fault diagnosis in internet of things systems, where multiple distributed components interact asynchronously through communication buffers, poses significant challenges due to system scalability and communication uncertainties. To address this, this paper studies the problem of diagnosability consistency in a discrete event system modeled using a labeled Petri net composed of several interconnected subnets via buffer places. Due to the state explosion problem, the diagnosability analysis by a centralized approach for large-scale systems is computationally demanding and sometimes even impossible. In this work, we assume that Petri net modules are connected through buffer places according to predefined rules and do not share transitions or resources, offering a complementary and computationally efficient alternative to existing modular approaches for large-scale systems. The diagnosability of subnets is analyzed with a particular automaton, called an unfolded verifier, by determining whether there exists a fundamental path that leads to the violation of the diagnosability. The proposed approach investigates the diagnosability of large systems with modular structures (namely global diagnosability), without constructing a global unfolded verifier, by analyzing the diagnosability of each module only (namely local diagnosability). More precisely, the consistency between the local diagnosability and the global diagnosability is addressed by determining whether all the fundamental paths of subnets survive in the global net due to the composition of subnets. Finally, an algorithm is given to deduce the diagnosability of a monolithic system. Compared with the existing centralized approaches, the complexity is practically mitigated by using the proposed one.

This paper addresses the diagnosability analysis problem under malicious attacks of a networked discrete event system modeled by a labeled Petri net. Astealthy replacement attackis considered to alter or corrupt the observation of the system, in which the transition labels are replaced by others or the empty string, and its attack stealthiness requires that the corrupted observations should be contained in the behavior of system. The objective of this work is, from an attacker’s viewpoint, to design such an attack for compromising theattack-induced diagnosabilityof a system. Specifically, a new structure, called an attack verifier, is constructed by integrating the attack behavior to enumerate all the attack paths to be transformed into fundamental ones that violate the attack-induced diagnosability. Then an optimal attack synthesis problem in terms of minimum energy cost is formulated by integer linear programming problems. An example of an automated manufacturing system is provided to show the efficiency of the proposed attack strategy compared with the existing approaches.

This work investigates the use of deep reinforcement learning to address the scheduling problem of identifying minimal control sequences while ensuring deadlock avoidance in transition-timed Petri nets. Traditional control strategies often depend on exhaustive search algorithms or heuristics, both of which tend to be computationally intensive and exhibit poor scalability as system complexity increases. In this study, we formulate the control sequence scheduling task as a Markov decision process and adopt the Deep Q-Network framework to learn control policies through interaction with an integrated timed Petri net simulation environment. The reward function is specifically designed to minimize total execution time, with penalties applied to extended durations, thereby guiding the learning process toward efficient and safe behaviors. In addition, we evaluate the robustness of the learned policy under structural perturbations (i.e., failed transitions) and temporal variations via scaled firing delays. Experimental results indicate that the proposed method consistently identifies control sequences with shorter makespans when compared to conventional approaches, offering significant improvements in both runtime and computational efficiency. Moreover, once the learned policy generalizes effectively, it can be reused to quickly generate feasible control sequences even under moderate perturbations, without requiring retraining. The comparative analysis further highlights these advantages, demonstrating the potential of the proposed reinforcement learning-based framework as a practical and scalable solution for optimizing control strategies in complex timed Petri net models. Two case studies on manufacturing systems are used to illustrated the efficiency of the proposed strategy.

This paper deals with the online fault diagnosis problem of discrete event systems under malicious external attacks. We consider a scenario where an attacker can intercept certain sensor measurements and alter them arbitrarily, potentially causing a diagnoser to malfunction. In the framework of labeled Petri nets, a novel integer linear programming problem is formulated by introducing binary variables to estimate the possible transition sequences of an observation that may have been tampered with by an attacker. The proposed approach makes two main contributions. The first one is that, by specifying two different objective functions to the integer linear programming problem, we can obtain the diagnosis results in the presence of attacks, which classic diagnosers may fail to achieve; the second is computational efficiency. In the absence of attacks, the proposed approach is experimentally verified to have lower computational overhead compared with the existing results that are based on integer linear programming and those using basis markings. Finally, the proposed approach is illustrated through a manufacturing system for assembling brake valves. Note to Practitioners—Fault diagnosis is critical for highly automated systems such as manufacturing systems, power plants and smart grids. Engineers are familiar with various fault diagnosis techniques in their community. However, malicious attacks in a system are not fully considered when performing fault diagnosis. This research elaborates upon a novel approach to fault diagnosis of discrete event systems modeled by labeled Petri nets, which can perform online fault diagnosis both in the presence and absence of attacks. The approach enables faults to be detected even after certain labels are tampered with by an attacker. The proposed diagnostic vehicle is presented in terms of integer linear programming problems, which facilitates its applications to real systems by practitioners.

The problem considered in this work concerns the control of hybrid systems, studied from the discrete event systems theory viewpoint. The objective is to compute a transient control trajectory for reaching a steady state from a given initial state. The hybrid systems are modeled by a class of hybrid Petri nets called controlled generalized batches Petri nets, which introduce variable delays on continuous flows for modeling and analysis of dynamical systems. The key contributions of this study are as follows: two event-driven control strategies are proposed for reaching a target steady state, offering advantages in terms of control actions and time performance. These strategies are based on ON/OFF state transitions, with the firing flow either limited to its steady flow or maximal flow; two algorithms are presented to implement these control strategies effectively; a case study of a bottling production line, a high throughput manufacturing system, is provided, demonstrating the application of the proposed methods and evaluating their efficiency in terms of time performance and the number of generated events. Note to Practitioners—In this work, two event-driven control strategies for reaching a steady state from a given initial state are presented. We use controlled generalized batches Petri nets that are suitable discrete event formalism for the modeling of complex systems such as transportation systems, high throughput production lines and, crowds behavior. This Petri net could model groups of moving entities with given forms (speed, density, length), which allows to consider variable delays of transfer elements due to congestion or groups merging. The objective is to reach a target steady state characterized by constant flows and also particular forms of the entities groups. This is a challenging issue because the existing formalisms and methods usually allow to reach a given steady setting without considering the forms of the entities groups. The proposed control strategies could be used, for example, during a recovery mode in order to reach the steady state after a system’s shutdown, failure or malicious attack. Their effectiveness is shown on the Perrier mineral water bottling production line.

This paper focuses on the modeling and analysis of systems with various temporal behaviors in the framework of discrete event systems modeled with time-dependent Petri nets. While Petri nets have been extensively studied, few existing formalisms effectively represent the coordination and synchronization among temporal behaviors. To this end, we first introduce a dual-time Petri net that captures both state-driven and event-driven behaviors by integrating temporal attributes associated with places and transitions, respectively. To describe the dynamic evolution of systems, a structural representation of the state space, abstracted as an extended state class graph, is presented. This representation serves as a foundation for analyzing critical system properties. Moreover, we show the efficiency of the proposed method to address the complexity in temporal dynamics, offering a more powerful modeling capability and a more compact structure compared with the existing time-dependent Petri net models. Finally, a case study on a semiconductor manufacturing system is provided to illustrate the practical application of the established model and reported analysis methods.

The fault diagnosis problem in discrete event systems consists in detecting the occurrences of faults in a plant, which is essential for ensuring the reliability of the plant. In the literature, this problem has been widely studied by assuming that the communications between a plant and a diagnostic agent, i.e., a diagnoser, are reliable and instantaneous. However, for a networked system, the information generated by a plant is transmitted through a shared communication network such that communication delays and losses are inevitable. This article formulates and studies the fault diagnosis problem in networked discrete event systems (NDESs) modeled by labeled Petri nets, where communication delays and losses are considered. Such a problem is also calledrobust fault diagnosisin this article. An important notion closely related to robust diagnosis, namednetworked diagnosability, is introduced, indicating that any occurred fault in a NDES is definitely determined after a limited number of observations. For a NDES, a tool called anetworked basis diagnoseris excogitated to solve the robust diagnosis problem. A necessary and sufficient condition for verifying the networked diagnosability of a plant is derived by using the developed diagnoser. Finally, a manufacturing system is presented to illustrate the developed approach.

This research focuses on the forbidden state problem in the framework of labeled Petri nets (LPNs), i.e., to design a supervisor for a plant modeled by an LPN such that the closed-loop system cannot reach a set of predefined forbidden markings and does not contain any deadlock. Different from the traditional control scheme, the supervisor derived by this work can not only observe the observable transitions, but also the quiescence information. First, a new structure named an extended basis reachability graph (EBRG) is introduced to describe the reachability space of an LPN without computing all reachable markings. Based on an EBRG, a basis observer is then excogitated to represent the behavior of an LPN. Some states in the basis observer are defined as bad states and control-induced deadlocks, which relates to the undesirable behavior of the plant. Finally, an algorithm is introduced to compute a supervisor based on the basis observer. The consideration of system quiescence provides extra information on the marking estimation of the closed-loop system such that certain disabled transitions are re-enabled. Consequently, the developed supervisor in this article is generally more permissive than those do not observe the quiescence.

This work addresses the security problem of protecting secrets in the framework of discrete event systems that are modeled by deterministic finite automata. We characterize a global secret that composes of one or multiple states, in which each state is assigned to a security level. A state is said to be protected if any event sequence from the initial state for reaching it contains the amount of protected events equal to or greater than the required security level. In addition, we assume that the protected event labels must be recovered within a bounded of consecutive protected events (called as$K$-protection). Our objective is to design a$K$-protection event policy such that the protected secret state pieces satisfy a predefined protection threshold. To this end, we first construct a security automaton that integrates the system state information and its current security level, and a$K$-protection automaton that lists all the possible protections of event sequences. Then by using the supervisor control theory technique, the valid protecting policy to enforce the security requirement is obtained. Finally, examples are used to illustrate the proposed protection method.