This paper proposes a reinforcement learning framework for dynamic secret protection in discrete event systems. We formulate the secret protection problem as a reinforcement learning task over automata. Compared with classical supervisory control theory, the proposed framework provides an automated approach for dynamic secret protection in the systems without requiring the explicit construction of a security automaton. During training, the agent explores protection and non-protection actions at each state. State-action pairs are penalized when secret states are reached with insufficient protection, and rewarded when security requirements are satisfied, while protection costs are also taken into account. Through interaction with the environment, the agent gradually learns an optimal protection policy. We implement and compare Q-learning and SARSA algorithms. Experimental results show that both methods achieve a high success rate and produce feasible protection policy. However, SARSA demonstrates higher training efficiency and better robustness.

This paper proposes an optimization-based approach for the risk evaluation of Autonomous Vehicles (AVs) integration using the Analytic Hierarchy Process (AHP). A set of Key Performance Indicators (KPIs) is aggregated into a Global Traffic Indicator (GTI) to compare an AV scenario with a traditional traffic scenario. The methodology consists of two steps. In the first step, an AHP originally defined for conventional traffic evaluation is adapted to the AV scenario through a lexicographic optimization that adjusts the KPI weights while preserving consistency with the original pairwise judgments and reducing the influence of unfavorable indicators. In the second step, using the adapted weights, an optimization model identifies the minimum set of KPI improvements required for the AV scenario to outperform the traditional one. A case study shows that improvements in a limited number of KPIs are sufficient to obtain a GTI advantage for AV deployment.

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. Note to Practitioners-Timed Petri nets are a widely adopted modeling formalism for capturing the routing, buffering, and resource-sharing logic inherent in manufacturing systems, transportation networks, and robotic cells, especially where temporal constraints are critical. In this work, the control problem is formulated as a Markov decision process, and a Deep Q-Network is trained in a simulated environment to learn a control policy that selects the next enabled transition, guiding the system toward a target marking while avoiding deadlocks and minimizing total execution time. Once training is complete, typically within minutes to a few hours on a single industrial-grade GPU, the learned policy can be exported as a lightweight module. This policy can be embedded into a programmable logic controller, edge device, or manufacturing execution system, enabling real-time control decisions within milliseconds. The resulting controller can respond immediately to dynamic conditions such as rush-order insertions, machine failures, or operational reconfigurations, eliminating the need for manual intervention or reprogramming. Empirical validation on practical benchmark scenarios, including flexible job-shop and assembly-line systems, demonstrates that the proposed method achieves significant reductions in both makespan and computational overhead compared to traditional heuristic or rule-based approaches, thereby offering a scalable and efficient solution for modern intelligent manufacturing environments.

The increasing complexity and uncertain system of modern discrete event system (DES) challenge traditional model-based control approaches, while artificial intelligence (AI) techniques offer powerful data-driven decision-making capabilities but lack formal guarantees. This review surveys recent research on the integration of AI with DES and supervisory control theory. Following a systematic literature mapping methodology, the literature is organized using a taxonomy based on three orthogonal perspectives: control and decision paradigm, system capability and property, and application and operational objectives. The review highlights how learning-based methods enhance adaptability and performance in DES, while also exposing persistent challenges related to safety, nonblocking behavior, data efficiency, and interpretability. By structuring existing approaches and identifying open issues, this review provides a coherent overview of the current research landscape and outlines key directions for future work on AI-enabled DES.

This work addresses the problem of protecting multiple global secrets in discrete event systems modeled by nondeterministic finite automata. Specifically, a global secret in a system is assumed to be composed of one or more states, each assigned a specific security level. We say that a state is protected if any sequence of events leading to it from the initial state contains a quantity of protected events that is equal to or greater than the required security level. Correspondingly, a global secret is said to be protected if the cumulative weight of its containing protected states (or all containing states are considered in the worst-case scenario) satisfies a user-defined protection threshold. Our objective is to develop an event protection policy that is capable of protecting global secrets. To do so, we build an augmented automaton which eliminates the difficulty of analyzing the infinite sequences when verifying protection. Then, an optimal protection policy with minimum cost can be obtained by solving an integer linear programming problem. Examples are given to illustrate the effectiveness of our proposed protection strategy.

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 article studies the problem of diagnosability consistency in a discrete event system (DES) modeled using a labeled Petri net (LPN) 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 using the proposed one.

This paper addresses the enforcement of prognosability and $K$-step prognosability in discrete event systems modeled with unbounded Petri nets that may enter deadlocks. Given an unbounded labeled Petri net, a simplified basis coverability graph is established to encode deadlock information without enumerating all basis markings. The enforcement of prognosability and $K$-step prognosability is achieved via optimal sensor selection using a relabeling function that maximizes the achievable $K$. Considering the cost of relabeling sensors, the proposed relabeling function is optimal by solving an integer linear programming problem. Examples are presented to demonstrate the proposed method.

Petri nets (PNs), developed in the early 1960s, have gained popularity since the 1990s as an effective method for modelling the behavior of complex systems. Starting from manufacturing systems, the first domain in which they have been successfully applied as an effective modelling and analysis tool, they have then established themselves as a modelling, analysis, control, and optimization framework in many other application fields. In this paper, an overview of applications of PNs in manufacturing, warehouse systems, transportation, robotic, and health care systems is presented. Finally, the implementation of discrete event controllers and supervisors by means of PN models on industrial control devices is discussed.

This paper presents a robust data-driven policy-update method for discrete-time linear quadratic regulation of unknown linear systems affected by bounded data disturbances. Input–state measurements define the set of dynamics consistent with the data, and state-feedback controllers are updated without identifying a nominal model. Each controller update is certified by a common quadratic Lyapunov function obtained from linear matrix inequalities derived through data-based elimination of the system matrices and Petersen’s lemma. A proximal redesign term centered at the current controller links consecutive controllers and yields a convex update for a fixed Petersen multiplier. The resulting procedure generates a sequence of controllers and returns a final controller Kf whose robust closed-loop stability is verified over the entire data-consistent model set. Closed-loop tests on a low-dimensional random test suite illustrate how the certified data-driven controllers empirically approach the model-based LQR performance computed on the true validation model, compare against one-shot and identification-based baselines, and include a proximal-term ablation.

This paper investigates the impact of static temporal parameters on the behavior of timed discrete event systems modeled using dual-time Petri nets. In such models, the firing of transitions is essential to ensure correct system evolution. However, improperly configured temporal constraints may result in dead transitions, where certain transitions are prevented from firing despite being enabled with respect to markings, thereby disrupting expected system behavior. To address this issue, we analyze the conditions under which dead transitions occur due to invalid temporal functions within the net structure. Based on this analysis, a set of adjustment options is introduced to resolve a dead transition, designed to restore an invalid firing window by modifying temporal parameters. Furthermore, we propose a cost-based adjustment strategy that iteratively derives a valid temporal function, ensuring the absence of dead transitions in the revised system. At each iteration, the strategy selects the adjustment option with the lowest associated cost to resolve a specific dead transition. To validate the effectiveness of the proposed approach, an extended state class graph is employed as a structural representation of D-TPN evolution, enabling verification of the resolution of dead transitions under each revised temporal function.

This paper studies risk-averse supervisory control of probabilistic discrete event systems under logical controllability constraints. Unlike existing optimal PDES supervision approaches that rely on expectation-based performance criteria, we address scenarios where rare but high impact losses must be explicitly mitigated. To this end, we combine a loss-averse stage cost transformation with a Conditional Value-at-Risk (CVaR) objective to capture both asymmetric sensitivity to undesirable events and tail-risk of cumulative system behavior. The resulting infinite horizon risk-averse control problem is approximated by a finite horizon formulation with explicit error bounds. Using a finite unfolding under logical constraints and an occupation measure representation, the CVaR minimization problem is reduced to a linear program. We further show that an optimal probabilistic supervisor can be constructed directly from the optimal flow variables.

This paper proposes a reinforcement learning (RL)-based framework for optimizing secret protection policies in discrete event systems, aiming to minimize protection costs while satisfying multi-level security requirements of secret states. In a nondeterministic finite automaton model, several secret states are defined and require protection under varying confidentiality demands. To address this, a reward function is designed to couple protection effectiveness with cost efficiency, guiding the agent to autonomously discover the lowest-cost protection sequence through a Markov decision process formulation. Two representative RL algorithms are employed in the experiments: Q-learning, a value-based method, and Vanilla policy gradient (REINFORCE), a policy-based method. Experimental results demonstrate that the proposed framework can effectively adapt to diverse security requirements while achieving efficient and cost-effective secret protection. Compared with classical supervisory control theory approaches, the RL framework exhibits more intelligent and efficient exploration capability, making it feasible to derive protection strategies for large-scale automata with numerous states and transitions. Moreover, the proposed method eliminates the need to construct security automata, thereby simplifying the computation procedure and providing a lightweight methodological foundation for secure system design.

This paper presents a method for enforcing temporal liveness in timed discrete event systems modeled with dual-time Petri nets, where temporal attributes are associated with both transitions and places. Temporal liveness is essential for ensuring the correct dynamic evolution of a system under temporal constraints. We establish sufficient and necessary conditions under which liveness violations occur due to an infeasible temporal function in dual-time Petri nets. To address these violations, a set of parameter tuning options, along with a tuning cost, is introduced to modify relevant static temporal parameters assigned by the temporal function. Then, two cost-based parameter tuning strategies are proposed to iteratively synthesize a feasible temporal function that ensures temporal liveness while minimizing the overall tuning cost. At each iteration, a single-option tuning strategy incrementally verifies individual tuning options for resolving temporal violations, while a multi-option strategy is formulated as a linear programming problem, enabling the simultaneous modification of multiple parameters among tuning options. The effectiveness of the proposed approaches is demonstrated through an example of a semiconductor manufacturing system, using an extended state class graph to verify that the revised system is free of temporal liveness violations. Furthermore, a comparative analysis of the two strategies highlights their respective trade-offs and offers practical relevance for real-world implementation.

To maximise energy independence from fossil fuels, an ambition strongly promoted by European regulations such as the EuropeanUnion (EU) Green Deal and the ’Fit for 55’ package, it is crucial to invest in new renewable energy sources (RES). Buildingmanagers now face a growing number of complex choices among a wide range of technologies, each with different cost structures,energy generation potential and spatial requirements. These options range from photovoltaic panels, which typically generate highlevels of electricity, to combined heat and power (CHP) systems, which are particularly effective in regions with significant heatingrequirements, and innovative vertical-axis wind turbines, which are designed specifically for urban rooftops. These technologies arebeing progressively integrated into buildings to reduce grid dependency, lower operating costs, and enhance overall sustainabilityperformance. However, given the diversity and complexity of these solutions, investment decisions can be challenging. To avoidsuboptimal choices, detailed evaluations of technical, economic, and spatial feasibility are essential. In this context, developingsophisticated decision-support tools is essential, as they help stakeholders to assess investment risks, compare alternative scenariosand determine the long-term economic viability of RES integration in buildings. This paper presents a comprehensive optimisationtool that provides building managers with data-driven recommendations for the most suitable renewable energy solutions for existingbuildings. The tool uses advanced algorithms to analyse building characteristics, local climate conditions, energy consumptionpatterns, and financial parameters to identify the optimal mix and size of renewable technologies that minimise the Cost–RevenueRatio (CRR), while satisfying physical constraints, self-consumption requirements and comfort requirements. The proposed approachadvances the state of the art towards a comprehensive decision-support platform for building energy investments by havingthe capacity to potentially embed tariffs directly in the objective function and integrate operational scheduling with long-terminvestment planning.

This paper addresses the problem of identifying Aortic Aneurysm, a pathological condition characterized by an enlargement of the aortic diameter that can cause various health issues and may sometimes lead to death. Using a dataset of Computed Tomography images from both healthy and affected patients, three advanced Convolutional Neural Network (CNN) architectures, ResNet50, VGG16, and InceptionV3, have been implemented and compared to predict and improve the automatic diagnosis of this disease through Artificial Intelligence, reducing the need for invasive examinations. To overcome the limited dataset size, an enhanced data augmentation and synthetic image generation approach have been applied during training to increase image diversity. The results demonstrate that ResNet50 achieves the highest validation accuracy of 95%, indicating its superior capability for identifying Aortic Aneurysm compared to the other evaluated models, while highlighting the potential of CNN-based deep learning methods for reliable, non-invasive Aortic Aneurysm identification.

In large organizations, the allocation of personnel within office spaces presents significant challenges, particularly with the adoption of modern working methodologies such as smart working, co-working, and agile working. This paper addresses the optimization of workspace assignments to balance occupancy levels while ensuring cohesion within organizational units and compliance with individual work schedules. The proposed approach incorporates constraints to prevent overcrowding, maintain consistent desk assignments, and enforce separation between specific personnel groups. A multi-objective Integer Linear Programming formulation is developed and validated through a real case study. Results demonstrate that the methodology effectively reduces peak occupancy imbalances and strengthens team cohesion, providing human resources departments with a practical decision-support tool that requires minimal technical expertise. The solution features an intuitive web interface that facilitates efficient space management in dynamic working environments.

This paper addresses the diagnosability analysis problem under malicious attacks of a networked discrete event system modeled by a labeled Petri net. A stealthy replacement attack is 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 the attack-induced diagnosability of 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. Note to Practitioners-This study highlights critical cybersecurity risks in automated manufacturing, particularly in networked discrete event systems. With increased reliance on multi-agent coordination, cyber threats such as stealthy attacks can compromise system diagnosability by corrupting event observations. Practitioners in industrial automation and cybersecurity must prioritize robust detection mechanisms to detect inconsistencies in sensor data and event labels. Securing communication channels and integrating resilient event-based monitoring frameworks can provide early warnings against cyber intrusions. In practical applications, the proposed attack verifier architecture and the integer linear programming based cost model offer a systematic method to identify system vulnerabilities, allowing practitioners to assess security gaps and determine which components require prioritized protection. At the deployment level, the verification process can be executed offline, while low overhead runtime monitoring of event label consistency can take place online to support anomaly detection. As manufacturing systems increasingly integrate automation and networked control, ensuring that robust diagnosability remains essential for safeguarding operational integrity and resilience.

This paper investigates opacity enforcement via publicly known and constrained edit functions under incomparable observations. We first formalize the notion of ik-enforceability, which combines admissibility, consistency, confidentiality, and integrity requirements. A game-theoretic synthesis framework is then developed, consisting of three pruning stages and one merging stage, including: (i) an edit game structure is constructed to capture all feasible constrained edit actions; (ii) problematic states that violate admissibility, confidentiality, or consistency are pruned; (iii) an identifying observer is employed to model the reverse-engineering capability of the intruder; and (iv) states are merged to ensure the consistency of edit actions under the observation of the defender. The resulting edit mechanism provides necessary and sufficient conditions for synthesizing ik-enforcing edit functions.

Robust perception and intelligent path planning are critical for reliable autonomous operation in robotics and autonomous vehicles (AVs), especially in complex environments. AVs must accurately analyze their surroundings, detect obstacles, and select safe routes, as even minor errors can cause collisions. Convolutional neural networks (CNNs) have greatly enhanced road understanding and real-time decision-making. This study integrates a CNN model into Stable Baselines 3 (SB3), enabling interaction with a SUMO simulation map to determine optimal routes using diverse metrics, including minimizing travel time, reducing congestion, avoiding traffic lights, preventing loops and dead ends, maintaining shorter distances to destination, and ensuring stable speeds. This addresses key limitations in prior research and supports more efficient and sustainable autonomous mobility. This work makes three main contributions. First, it introduces a multi-input CNN with a VGG-like backbone capable of fusing spatial traffic features with scalar speed data for path planning. Second, it identifies shortcomings in existing CNN-based approaches, including limited multi-modal fusion, insufficient handling of traffic-light congestion, and inadequate loop-avoidance mechanisms. Third, empirical evaluation in SUMO shows that multi-input fusion yields more stable predictions and superior routing compared to single-input CNN baselines, demonstrating the value of multi-modal deep learning for autonomous mobility.

AI-native, programmable, and disaggregated 6G networks will be highly dynamic and distributed, demanding tools that can explain, predict, and safely optimize behavior across the edge–cloud continuum. Network Digital Twins (NDTs) promise this capability, yet current efforts in research and industry are fragmented and lack widely accepted formal definitions and architectural guidelines. This paper proposes a structured framework for NDTs in 6G, addressing these gaps by refining the conceptual foundations of NDTs, introducing a functional architecture, inherited from the 6G-TWIN EU consortium, and clarifying key components such as AI-driven workflows, the place of simulation, data management, and orchestration. Concrete examples illustrate how these components enable network automation, optimization, and predictive analytics. The paper proceeds by reviewing related work and standardization efforts, specifying functional and non-functional requirements, presenting the architecture and its various domains, and detailing lifecycle management across cloud to edge. We then report early implementations and evaluation results, and discuss security, privacy, and governance considerations, concluding with directions for validation and uptake. The key objective is to offer a cohesive reference model that guides the community in shaping NDT development, ensuring interoperability, scalability, adaptability, and seamless integration into AI-native 6G networks for improved intelligence and efficiency.