Keywords: Supervisory Control Theory, Automata, Applications
Abstract: Smart contracts are computer programs executing in a blockchain environment, that can enforce agreements among mutually distrusting users without the involvement of any trusted third party. However, smart contracts may implement bias towards or against certain users, either intentionally or mistakenly by improper coding. Such bias may also manifest through multiple users colluding to put other users at a disadvantage. This study proposes a methodology to use supervisor synthesis to detect such biases in smart contracts. Given an extended finite-state machine model of a smart contract, by selecting which events are considered to be controllable, the perspective from which bias is considered can be decided, and by marking states, positive as well as negative bias can be captured. The existence of a supervisor may then reveal the existence of bias. The method is demonstrated on a multi-player game-based smart contract. The analysis shows that there does not exist positive bias towards any single player, that is, there is no guaranteed winning strategy for any single player. However, colluding players may enact negative bias against the other players, thus, there is negative bias against other players so that they may lose the game irrespective of their actions.

Keywords: Supervisory Control Theory, Automata, Applications
Abstract: User-centric discrete-event system are discrete-event systems with which multiple users interact, each through their own distinct events. Each user has specific goals that they want to achieve, represented by specific states of the discrete-event systems. In these kinds of systems, bias may be present, positive bias that allows some users to always achieve their goals irrespective of other users, or negative bias that prevents some users from achieving their goals irrespective of what they do. This work shows how the existence of a strategy, a special type of supervisor computed according to the Ramadge & Wonham supervisory control theory, can with carefully chosen controllable events and marked states reveal bias, positive and negative, in a user-centric discrete-event system. This can then be a guiding factor in deciding whether to interact or not with a given user-centric discrete-event system.

Keywords: Max/plus-algebra, Discrete event simulation, Petri nets
Abstract: This paper proposes a global Just-in-Time control synthesis for traffic light networks modeled as Max-Plus Linear Systems. Unlike decentralized local strategies that manage synchronization and exclusion constraints separately, the proposed approach unifies these requirements into a single algebraic framework involving geometric constraints on the state space. We develop a centralized controller that optimizes the firing times of all transitions, maximizing traffic flow by delaying red phases until safety or synchronization strictly demands them. Simulation results compare the proposed global synthesis against a standard local control strategy under both nominal and failure conditions. The analysis demonstrates that the global controller exhibits superior robustness, avoiding unnecessary signal locking during disturbances and maintaining operational efficiency where local logic fails. The findings confirm that the algebraic centralization provides a flexible coordination mechanism for urban traffic networks.

Keywords: Max/plus-algebra, Petri nets, Performance evaluation, optimization
Abstract: The objective of this article is to Evaluate the Performance of Tropical Discrete Event Systems. These systems are subject to synchronization and delay phenomena and are described using dater functions in the max-plus semiring, which is a particular instance of Tropical algebra. They are graph- ically depicted by Timed Event Graphs, a subclass of timed Petri Nets. In the literature, Performance Evaluation, more precisely, the throughput, is typically addressed by studying the Spectral problem of an event-invariant system matrix. This article examines the case where the system matrix is event- varying but constrained within a polytropic (Tropical polytopic) set. We solve an extended spectral problem based on residuation theory to determine an initial condition that ensures the system is balanced, meaning that the instantaneous cycle time remains bounded and free of token accumulation. To illustrate the approach, a Performance Evaluation of a small Rail network is conducted.

Keywords: Max/plus-algebra, Scheduling, Applications
Abstract: This paper presents an event-based scheduling framework for hospital robot fleets using Switching Max-Plus Linear (SMPL) models. The model captures routing decisions, coordination of shared resources (e.g., elevators), and batching of packages into transport rounds, which implicitly assigns packages to robots. To deal with execution-time variability and newly arriving transport requests, we use a receding-horizon rescheduling scheme that repeatedly re-optimizes the switching decisions during execution, considering computation times in advance. Simulations on a simplified hospital layout show that the method can adapt online to travel-time variability and can revise future routing, resource ordering, and batching decisions when new urgent requests arrive.

Keywords: Supervisory Control Theory, Automata, Observability
Abstract: In this paper, we develop a data-driven approach for marking nonblocking supervisory control of discrete-event systems (DES). We consider a setting in which the plant model is structure-unknown, while a set of behavioral data is available. Our objective is to determine: Under what conditions on the available data can a valid marking nonblocking supervisor be synthesized for the structure-unknown DES so as to satisfy a given specification? To address this question, we introduce a new concept called marking data-informativity, which extends an existing data-informativity concept. Moreover, we establish a necessary and sufficient condition characterizing this concept, and we design an algorithm for verifying whether a given data set is marking informative. When the available data fails to be marking informative, we further study restricted marking data-informativity, which allows a valid supervisor to be synthesized for a restricted sublanguage of the specification. Finally we develop a method to compute the largest subset of control specification for which the data set is least restricted marking informative.

Keywords: Diagnosis, Max/plus-algebra, AI-integration in DES
Abstract: In this paper, we introduce a consistency-based diagnosis algorithm over max-plus linear systems that is fully data-driven. We first exploit a method for learning offline diagnosis models from event data available through unlabeled logs. Then we propose to use these models online to perform time failure diagnosis over max-plus linear systems. The properties of the method are presented, as well as results from a simulated illustrative example.

Keywords: Identification, Diagnosis, Applications
Abstract: Current data-driven fault detection methods in microgrids often rely on black-box machine learning models, lacking semantic interpretability. To address this issue, this paper proposes a hybrid framework bridging the gap between continuous signal processing and discrete event system interpretability. By combining K-means clustering with the Event-Based Automaton Model (EBAM), the proposed method abstracts continuous operational variables into a symbolic finite-state automaton. This approach enables the identification of the system’s nominal logic without requiring physical parameter estimation. The methodology was validated using synthetic datasets generated via pandapower, evaluating 15 distinct fault classes (sensor, actuator, and logic violations) across multiple environmental conditions. Experimental results demonstrate that while a model trained exclusively on sunny days achieved a precision of 76.74%, it generated false alarms under unobserved weather conditions. However, when the training domain was expanded to include cloudy and rainy profiles, the model’s precision rose to 100%, and accuracy improved to 77.14%, confirming the framework’s capability to effectively distinguish environmental power fluctuations from technical faults. Despite this robustness, a stable recall of 68.00% highlighted the intrinsic limitations of event-driven abstractions in detecting stationary faults. Ultimately, the results validate the EBAM as a highly interpretable and lightweight diagnostic tool suitable for low-cost embedded controllers.

Keywords: Supervisory Control Theory, Automata
Abstract: This paper surveys recent advances in supervisory control theory since its 30th anniversary in 2017. We performed a systematic literature search and selected 272 relevant papers, with a focus on automata-based approaches. These were fitted into coherent narratives, based in part on a taxonomy of supervisor synthesis methods. The obtained papers show the fast and vast progress of the field, where recent research covers a wide range of new synthesis optimization techniques, different aspects such as fault tolerance, security, and timing, and new and diverse application domains. This survey refrains from in-depth descriptions of techniques, instead focusing on high-level contributions of recent works, how they relate to each other, and future directions for research.

Keywords: Supervisory Control Theory, Observability, Applications
Abstract: In hierarchical supervisory control of discrete event systems, the observer property of the reporter map ensures that the high-level supervisor can rely on the occurrence of any event that is eligible in the high-level plant to implement a nonblocking closed-loop system. When combined with strict output control consistency and marking consistency, the observer property is a sufficient but not necessary condition for strong hierarchical consistency, which guarantees that the high-level model maintains the necessary information to achieve optimal nonblocking supervisory control for any high-level specification. Aiming to weaken the observer condition, this paper introduces the definitions of prefix-closing alphabet and of reliable events. The first main result demonstrates that it is sufficient to verify if the subset of reliable events is prefix-closing for the high-level controllable specification. A second result proves that nonblocking hierarchical supervision is ensured for any high-level specification if the set of uncontrollable high-level events is reliable and prefix-closing for the high-level plant. The application to the hierarchical structure of a valve circuit in process control where the reporter map is not an observer demonstrates that the novel conditions can be useful in practice.

Keywords: Supervisory Control Theory, Automata, Opacity
Abstract: This paper considers discrete event systems that are modeled as nondeterministic finite state automata and are subject to a bounded number of state attacks. A state attack allows an intruder to learn whether the current state of a system resides (or not) in a certain subset of states, called attack states. Assuming that the total number of state attacks at the intruder's disposal is bounded by a positive integer, this paper focuses on the synthesis of a resilient supervisor that prevents the intruder from inferring that the state of the system definitely resides within a subset of critical states, called secret states. The challenge is that the bounded number of state attacks can be performed whenever the intruder chooses. Regarding the supervisor ability, two scenarios are examined: (1) the supervisor is not aware of the initiation of state attacks or their outcome, and (2) the supervisor is aware of the initiation of each state attack but cannot obtain its outcome. For each scenario, we propose a minimally restrictive supervisory strategy and also provide elucidating examples to illustrate the corresponding methods.

Keywords: Automata, Diagnosis, Supervisory Control Theory
Abstract: This paper investigates diagnosability enforcement for discrete event systems modeled by deterministic finite automata. We first establish that diagnosability is equivalent to the normality of the union of the non-faulty language and a prefix of the faulty language, and we prove the existence of the supremal diagnosable and normal sublanguage. Building on this result, two dual supervisory-control approaches are developed: Active diagnosis and safety enforcement. For the former, we compute the supremal controllable, normal, and diagnosable subplant, while for the latter, we enlarge the faulty language by reclassifying a minimal set of non-faulty strings as faulty such that the resulting system becomes diagnosable with respect to the new faulty language. Finally, the safety-enforcement framework is extended from monolithic to modular discrete event systems. Illustrative examples are provided to demonstrate the effectiveness of the proposed methods.

Keywords: Automata, Supervisory Control Theory
Abstract: This paper studies risk-averse supervisory control of probabilistic discrete event systems (PDES) 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.

Keywords: Supervisory Control Theory, Cyber-security, Automata
Abstract: This paper investigates the problem of attack synthesis in the supervisory control of discrete event systems using ALTER model. The ALTER model is capable of modeling a wide range of sensor attacks, including deletions, insertions, replacements, and all-out attacks by describing possible attacks through the corresponding attack languages. We study the synthesis of sensor and actuator attacks, focusing on two key objectives: stealthiness and safety compromise. Necessary and sufficient conditions for the existence of such attacks are provided, along with methods to synthesize attacks when these conditions are met. The results advance the understanding of cyber attacks in discrete event systems and provides tools to ensure cyber security in supervisory control.

Keywords: AI-integration in DES, Verification, validation, test, Automata
Abstract: This paper addresses the problem of property estimation in timed probabilistic discrete event systems. The considered properties are state-based, meaning that the property depends on the states reached along the system’s execution. The main contribution of this paper lies in proposing general procedures for developing an artificial neural network–based approach for property estimation over time. It is assumed that no formal model of the system is available, instead, a dataset describing the system’s timed operational history is used. This dataset is exploited to train an artificial neural network that takes both logical and temporal information gathered during the system’s operation as inputs. The network outputs the probability that the property under investigation is currently satisfied. The paper details the procedures for data preprocessing, model development, and implementation. Finally, an application to secret disclosure estimation is presented.