This paper aims to present a unified optimization for resource allocation and scheduling in resource allocation systems. In contrast to traditional two-stage methods, which optimize scheduling and resource allocation independently, this study combines the two to produce globally optimal solutions within practical limitations. In order to describe various resource categories and their disparate quantity needs, a variable timed Petri net is created, in which the arc weights and time delays are determined by resource types. The problem is formulated as a budget-constrained makespan minimization model, with constraints linearized if possible. To handle an inherent non-linear constraint, an iterative mixed integer linear programming approach is developed to obtain optimal resource allocation and scheduling strategies. Extensive computational experiments verify that the proposed framework effectively determines optimal resource type and quantity configurations along with scheduling strategies, jointly minimizing makespan under budget constraints and demonstrating practical efficiency and applicability.

Resource allocation systems are considered fundamental to many practical applications, where the challenge is often posed by the need to optimize resource usage under budget constraints to improve system performance. In this paper, a systematic approach to resource allocation in Petri net-based systems is presented. First, a method for system bottleneck identification is analyzed to reveal the structural limitations affecting throughput. Based on this, the minimum number of resources required to maximize system throughput without budget constraints is determined. Subsequently, a heuristic iterative resource allocation strategy is developed, in which mixed-integer linear programming is employed to guide the allocation process considering budget levels. The effectiveness of the proposed method is demonstrated through comparative experiments under different resource constraints.

In this paper, we focus on two properties related to the privacy of partially observable discrete event systems: state-trajectory opacity and initial-state opacity. Both properties are trajectory-dependent, meaning that if a trajectory violates the property, all of its continuations will also violate it. Our contribution lies in demonstrating that the verification of these two properties can be addressed using the notion of fault diagnoser. Specifically, we define two ad hoc automata — one for each property — and show that, by analyzing their respective diagnosers, the properties can be verified. While the complexity of our method is the same as that of other state of the art procedures, our approach opens the door to tackling complex problems by combining approaches developed within two areas of opacity and diagnosis.

In this paper, we study the problem of fault diagnosis in Switching Output Automata (SOA), which is a formal modeling framework particularly suitable for describing artificial systems with discrete or quantized piecewise continuous outputs. We introduce Switching Output Automata with Faults (SOAF), an extension of SOA that incorporates timed fault arcs to model fault occurrences under specific temporal constraints. In our framework, faults are defined with respect to both the discrete states and the system outputs, where each fault occurrence is constrained to specific time intervals determined by the current global state of the system. To perform fault diagnosis, we introduce the Evolution Automaton with Faults (EAF), a nondetermistic finite automaton that serves as a logical abstraction of the SOAF. Based on the approach of Sampath and Lafortune, we construct a diagnoser for EAF that effectively performs fault diagnosis in the SOAF framework.

In this paper, the problem of cyber-attacks detection in timed probabilistic discrete event systems via artificial neural networks is investigated. We extend the problem of state estimation for timed probabilistic discrete event systems using artificial neural networks, to address attack detection. So that, a detection strategy is implemented to determine whether the system is operating in normal mode or under attack, and to identify the potential type of attack. Two primary cases are examined: (i) attack detection over observations. In this case, the attack detector recognizes whether the system is in a normal mode or an attack mode after each new observation, (ii) attack detection over time. Here, the attack detector evaluates the system’s status at each clock time increment.

In the hierarchical control, a system could be monitored by high-level and low-level users, who may obtain different information even if both know the structure of the system. Low-level users can only observe the occurrence of a subset of events, while high-level users can observe the occurrence of all the events affecting the system dynamics. A system is said bisimulation strong non-deterministic non-interferent (BSNNI) if low-level users can neither infer the occurrence of high-level transitions, nor infer the nonoccurrence of high-level transitions. In this paper, we focus on BSNNI analysis and enforcement of bounded Petri nets. We show that, under the assumption of acyclicity of the high-level subnet, the notions of basis marking and basis reachability graph (BRG) allow to solve such problems with clear advantages in terms of computational complexity since they prevent exhaustive marking enumeration.

This paper presents a data-driven experimental approach to identify models and design efficient automation strategies that optimize the drying-cooling process of 2D-shaped bread during the redesign of low-automated production systems. Thin-layer drying-cooling equations are shown to be suitable for describing the water and heat transfer dynamics in flatbreads. These equations can be used to predict the time required to achieve desired levels of moisture and temperature as a function of external temperature. This knowledge is then used to derive a discrete-time model of the drying-cooling process, which helps identify the most suitable re-engineering actions to improve production and quality while reducing waste. The case study involves a bakery that produces Carasau bread, which is a flat and dry bread typical of the Sardinian tradition with a long history and renewed interest in recent years. In this scenario, the drying-cooling process occurs during transportation via conveyor belts. We discuss how the process can be optimized using real-time measurements an adaptative control of the speed given the length of the conveyor belt. This represents a significant step forward in automating the manufacturing process of Carasau bread.

We present a new discrete event model called switching output automaton where with each state is associated a set of discrete output values. The evolution of such a system, as state and output change, produces as observation a piecewise constant signal. The goal of this paper is that of designing a suitable observer for estimating the current discrete state of this model as a function of the observed output signal. In addition, we show how the observer can be used to verify if the system is current-state opaque.

Railways are a well-recognized sustainable transportation mode that helps to satisfy the continuously growing mobility demand. However, the management of railway traffic in large-scale networks is a challenging task, especially when both a major disruption and various disturbances occur simultaneously. We propose an automatic rescheduling algorithm for real-time control of railway traffic that aims at minimizing the delays induced by the disruption and disturbances, as well as the resulting cancellations of train runs and turn-backs (or short-turns) and shuntings of trains in stations. The real-time control is based on the Model Predictive Control (MPC) scheme where the rescheduling problem is solved by mixed integer linear programming using macroscopic and mesoscopic models. The proposed resolution algorithm combines a distributed optimization method and bi-level heuristics to provide feasible control actions for the whole network in short computation time, without neglecting physical limitations nor operations at disrupted stations. A realistic simulation test is performed on the complete Dutch railway network. The results highlight the effectiveness of the method in properly minimizing the delays and rapidly providing feasible feedback control actions for the whole network.Note to Practitioners—This article aims at contributing to the enhancement of the core functionalities of Automatic Train Control (ATC) systems and, in particular, of the Automatic Train Supervision (ATS) module, which is included in ATC systems. In general, the ATS module allows to automate the train traffic supervision and consequently the rescheduling of the railway traffic in case of unexpected events. However, the implementation of an efficient rescheduling technique that automatically and rapidly provides the control actions necessary to restore the railway traffic operations to the nominal schedule is still an open issue. Most literature contributions fail in providing rescheduling methods that successfully determine high-quality solutions in less than one minute and include real-time information regarding the large-scale railway system state. This research proposes a semi-heuristic control algorithm based on MPC that, on the one hand, overcomes the limitations of manual rescheduling (i.e., suboptimal, stressful, and delayed decisions) and, on the other hand, offers the advantages of online and closed-loop control of railway traffic based on continuous monitoring of the traffic state to rapidly restore railway traffic operations to the nominal schedule. The semi-heuristic procedure permits to significantly reduce the computation time necessary to solve the rescheduling problem compared with an exact procedure; moreover, the use of a distributed optimization approach permits the application of the algorithm to large instances of the rescheduling problem, and the inclusion of both the traffic and rolling stock constraints related to the disrupted area. The method is tested on a realistic simulation environment, thus still requires further refinements for the integration into a real ATS system. Further developments will also consider the occurrence of various simultaneous disruptions in the network.

The radio block center (RBC) is one of the most essential ground systems in a high-speed train control system both in Europe and in China. The RBC handover procedure is an important function of RBC, which affects the transport efficiency, reliability and safety of railways. Analysis of crucial states in the RBC handover procedure is helpful to determine whether there are potential risks in the procedure, and to locate the fault in time when a fault occurs. In this paper, we study a property, called C-detectability, of the RBC handover. This property has been defined in discrete event systems and requires that the crucial states can be determined uniquely by observing the system output. Taking the RBC handover procedure in the Chinese train control system level 3 (CTCS-3) as an example, we first model the RBC handover procedure using Petri nets, which are a graphical and mathematical modeling tool to formalize the behavior of discrete event systems. Then, based on the notion of basis reachability graph, an efficient approach is used to check C-detectability of the Petri net modeling the handover procedure.Note to Practitioners—The railway system is a safety-critical system. System safety is essential to the railway system. It is necessary to provide formal methods to model the system and analyze its properties. The motivation of this work is to present a general modeling framework of railway systems for the crucial states estimation. The crucial states estimation of the railway system has not been discussed yet in the literature despite its importance due to its relationship with the safety of the railway. In particular, estimating the crucial states in the railway system helps to determine whether there are potential risks in the system. In this paper, we investigate a new state estimation property (C-detectability), which is related to fault diagnosis, marking estimation and fault identification. Future research will consider the use of timed Petri nets to increase the modeling power and to allow the performance analysis of the railway system.

In cyber–physical systems (CPSs), it is of great importance to handle network attack issues. In this article, we consider the supervisory control layer of CPSs, focusing on closed-loop control systems vulnerable to sensor-reading modification attacks (SM-attacks), which may disguise the occurrence of an event as a different event by modifying appropriately sensor readings in sensor communication channels. In particular, we consider the plant modeled as a bounded Petri net and the control specification consisting in liveness enforcing. Based on repeatedly computing a more restrictive liveness-enforcing supervisor under no attack and constructing a so-called basic supervisor, a method that synthesizes a liveness-enforcing supervisor tolerant to an SM-attack is proposed.

In this paper we consider timed automata endowed with a single clock that is reset at each event occurrence. A time interval is associated with each transition specifying at which clock values it may occur. We assume that the (logical and timed) structure of a timed automaton is known, and event labels associated with transitions are not observable. The problem addressed in this paper is to estimate and update the set of possible current discrete states as time elapses without any observation being received. By a partitioning of time intervals into regions, we design a λ-observer (λ is the null observed sequence) that, for a given state and a current time value, estimates the set of possible current states and the corresponding regions to which the timer value associated with each possible current state may belong.

This article proposes a novel methodology for multistage, multiproduct, multi-item, and closed-loop Supply Chain Network (SCN) design under uncertainty. The method considers that multiple products are manufactured by the SCN, each composed by multiple items, and that some of the sold products may require repair, refurbishing, or remanufacturing activities. We solve the two main decisions that take place in the medium-/short-term planning horizon, namely partners’ selection and allocation of the received orders among them. The partners’ selection problem is solved by a cross-efficiency fuzzy Data Envelopment Analysis technique, which allows evaluating the efficiency of each SCN member and ranking them against multiple conflicting objectives under uncertain data on their performance. Then, according to the estimated customers’ demand, the order allocation problem is solved by a fuzzy bargaining game problem, where each SCN actor behaves to simultaneously maximize both its own profit and the service level of the overall SCN in terms of efficiency, costs, and lead time. An illustrative example from the literature is finally presented.Note to Practitioners—We present a decision tool to address the optimal design, performance evaluation, and continuous improvement of modern cooperative SCNs. We propose an effective method to jointly solve the members’ selection and the orders’ allocation, considering the complex structure of modern SCNs, the multiobjective nature of the problems, and the uncertainty characterizing economic markets. Competition within SCNs stages and cooperation along the chain are considered, with the aim to improve both financial and environmental sustainability, while ensuring the highest service levels to customers.

The real-time rescheduling of railway traffic in case of unexpected events is a challenging task. This is mainly due to the complexity of the railway service, which has to ensure safety, punctuality, and efficiency to customers by respecting timetable, framework, and resources constraints. Most of the available researches focus on short delays (i.e., disturbances). Approaches typically rely on simplified macroscopic models for large-scale systems or detailed microscopic models for one or a few lines, due to the long computation time required for solving the rescheduling problem. Only a small number of works consider rescheduling in case of long delays (i.e., disruptions) and all of them are also based on either a macroscopic or a microscopic model. This research focuses on disruptions and aims at filling the gap between macroscopic and microscopic modelling by proposing an innovative bi-level rescheduling algorithm based on a mesoscopic Mixed Integer Linear Programming (MILP) model. The technique allows obtaining a feasible rescheduled timetable in a short computation time respecting not only timetable and safety constraints (typical of macroscopic models) but also capacity and ordering constraints for the disrupted stations (typical of microscopic models). The bi-level algorithm first solves the macroscopic MILP rescheduling problem and then, considering the cancellation and non-admissible platform assignments results, it solves a mesoscopic MILP rescheduling problem. This allows to significantly reduce the search space and consequently the computation time. The method is tested for the rescheduling of the Dutch railway traffic in case of a full blockade between two consecutive stations.

This paper provides a summary of my plenary talk at the 24th Int. Conf. on Emerging Technology and Factory Automation. It provides a survey (clearly, non exhaustive) of the main contributions dealing with the application of Petri nets in the manufacturing domain. In particular, it is shown how Petri nets have been efficiently used as a tool for modeling and simulation, analysis, and control of automated manufacturing systems. Future trends and open issues are discussed.

Cyber-physical systems have emerged as a key technology in the development of distributed and autonomous large scale systems. However, one of their undesirable side effects is the fact that they are particularly exposed to cyber attacks carried out by malicious intruders. Therefore, efficient strategies for cyber security are in high demand. In this paper, we consider the issue of attack detection in the framework of partially observable discrete event systems modeled by finite automata. We assume that the observation produced by a plant can be corrupted by an intruder which, through one or more attack dictionaries, can change events into different strings. The problem we address is that of detecting if a plant has been attacked and, if such is the case, of identifying the nature of the attack, i.e., which attack dictionaries have been used. We show that the problem of attack detection can be reduced to a classical problem of state estimation or fault diagnosis for a new structure which describes the behavior of the plant under attack.

In this paper, we propose a method to analyze diagnosability of bounded Petri nets with arbitrary labeling functions. The notion of basis marking is employed to avoid exhaustive enumeration of the set of reachable markings. The novelty consists in removing an assumption that is common in this framework, namely the Petri net system is deadlock-free after the occurrence of any fault. A finite state automaton, called DF-Verifier, is constructed, which allows one to perform diagnosability analysis by looking at some special cycles and states.

The problem of stealthy attacks for partially-observed discrete event systems is considered. An operator observes the plant through an observation mask that does not allow him to detect the occurrence of certain events (silent events). The observation is corrupted by an intruder who can insert and erase some sensor readings. We construct an attack structure A which guarantees that, when the plant reaches an unsafe state, A can make the operator think that the plant is in a safe state. Based on A, we can obtain a stealthy attack structure As by simply removing from A all the exposing states, all the weakly exposing states and their input and output arcs. The stealthy attack structure As only contains the possible attacks that can not be detected by the operator.

This work focuses on a class of Petri nets (PNs) called Weighted Systems of Simple Sequential Processes with Resources (WS3PR). We study how to enforce liveness to WS3PR by appropriately allocating resources. A sufficient condition that guarantees liveness of a net system in this class is first derived. Then, based on such a condition, we propose an algorithm that computes an initial marking of resource places that guarantees the liveness of a WS3PR system where the initial marking of the idle places is given. Note that, we do not guarantee that the resulting solution is optimal, in the sense that a smaller initial marking of resource places that still leads to liveness could exist. However, several numerical examples show that the solution resulting from the proposed approach is optimal.

The benefits of logistics and transportation systems to citizens, economy, and society can strongly increase when considering a smart, safe, and environmentally friendly management. This results in the implementation of intelligent transportation systems that combine innovative technologies and transportation frameworks at the aim of finding proper solutions to the related decision problems. To achieve such a goal, the intrinsic discrete event dynamics of these systems should be considered when deriving a model to be used for simulation, analysis, optimization, and control. Among the different discrete event models, Petri Nets (PNs) are particularly effective due to a series of relevant features. In addition, several high-level PN models (e.g., colored, continuous, or hybrid) allow the solution of complex and large-dimension problems that typically arise from real-life applications in the area of freight logistics and transportation systems. This paper presents a survey on contributions in this area. Papers are classified according to the addressed problem, namely, strategic/tactical or operational decision-making-level problem, and the adopted PN formalism. We also debate the approaches' viability, discussing contributions and limitations, and identify future research directions to enhance the successful application of PNs in freight logistics and transportation systems.

The main contribution of this correspondence paper consists in a linear algebraic characterization of the admissible marking set relative to a Petri net with uncontrollable transitions, subject to a linear constraint. In more detail, given a linear constraint that limits the number of tokens in one place, an algorithm is proposed to compute an approximation of the admissible marking set in terms of a disjunction of transformed linear constraints. The optimality of the solution is guaranteed provided that certain conditions are satisfied during the intermediate steps of the iterative approach. In all the other cases, the set of markings described by the transformed constraints could be surely contained in the admissible marking set.

In this paper, we present a decision support tool to optimize two of the most critical activities in intermodal railroad container terminals, in an iterative and integrated framework devoted to the terminal profit improvement. First, the model allows optimizing the freight trains composition, maximizing the company profit, while respecting physical and economic constraints, and placing in the train head/tail containers prosecuting to subsequent destinations. Hence, based on the resulting train composition, the decision support system allows optimizing the containers allocation in the terminal storage yard, in order to maximize the filling level while respecting physical constraints. The model is successfully tested on a real case study, the inland railroad terminal of a leading Italian intermodal logistics company.

This paper presents a train load planning technique for intermodal rail-road terminals. The proposed method aims at maximizing the train commercial value while respecting priority, physical, financial, and prosecution constraints (i.e., taking into account containers that prosecute their trip after the first destination). The approach consists of two phases: 1) modifying a previous approach by some of the authors, a linear integer programming problem is solved to maximize the train commercial value, keeping into account urgencies and priorities; 2) hence, a heuristics is used to take into account prosecuting containers and reduce the number of wagons to be re-handled. The technique is tested on a real case study and compared with the previous strategy proposed by some of the authors to show its effectiveness and ease of application.

In this paper consensus in second-order multi-agent systems with a non-periodic sampled-data exchange among agents is investigated. The sampling is random with bounded inter-sampling intervals. It is assumed that each agent has exact knowledge of its own state at any time instant. The considered local interaction rule is PD-type. Sufficient conditions for stability of the consensus protocol to a time-invariant value are derived based on LMIs. Such conditions only require the knowledge of the connectivity of the graph modeling the network topology. Numerical simulations are presented to corroborate the theoretical results.

In this paper we consider the problem of designing a state feedback controller for a labeled Petri net whose initial marking is known to belong to a given convex set. We allow for silent transitions (i.e., transitions labeled with the empty word) and indistinguishable transitions (i.e., transitions sharing the same label with other transitions). Transitions that are neither silent nor indistinguishable, are said to be observable since the observation of their label univocally identifies them. Moreover, we divide the set of observable transitions into controllable and uncontrollable (all unobservable transitions are obviously uncontrollable). Based on our previous results on marking observation in the above setting, we show how to derive, at design time, a state feedback control law; this way, the most burdensome part of the computations, is performed off-line.

In this paper consensus in second-order multi-agent systems with a non-periodic sampled-data exchange among agents is investigated. The sampling is random with bounded inter-sampling intervals. It is assumed that each agent has exact knowledge of its own state at all times. The considered local interaction rule is PD-type. The characterization of the convergence properties exploits a Lyapunov-Krasovskii functional method, sufficient conditions for stability of the consensus protocol to a time-invariant value are derived. Numerical simulations are presented to corroborate the theoretical results.

In this paper we present a decision support scheme to help managing and optimizing two critical activities in intermodal terminals, namely the containers allocation in the terminal yard and the freight trains composition. In particular, the focus of this paper is on the first problem and the goal is that of maximizing the utilization of the available space while keeping into account several constraints. The approach was successfully tested on a real case study, the rail-road terminal of a leading intermodal logistics company.

In this paper, we focus on labeled Petri nets with silent transitions that may either correspond to fault events or to regular unobservable events. We address the problem of deriving a procedure to determine if a given net system is diagnosable, i.e., the occurrence of a fault event may be detected for sure after a finite observation. The proposed procedure is based on our previous results on the diagnosis of discrete-event systems modeled with labeled Petri nets, whose key notions are those of basis markings and minimal explanations, and is inspired by the diagnosability approach for finite state automata proposed by Sampath in 1995. In particular, we first give necessary and sufficient conditions for diagnosability. Then, we present a method to test diagnosability that is based on the analysis of two graphs that depend on the structure of the net, including the faults model, and the initial marking.

The 12 papers in this special section can be divided into two sets. The first eight papers deal with general DES control problems, while the second set of four papers addresses other particular DES problems such as diagnosability analysis, state estimation, deadlock avoidance and testing.

A remark related to our recent paper is made. Using a counterexample we show that we need more strict assumptions with respect to those used to prove that if a system is diagnosable in a decentralized setting, then it is also diagnosable in a centralized one. Specifically, we require that the central diagnoser sees all the events that can be seen by all the local diagnosers, and that the central diagnoser can distinguish all observable events that the local diagnosers can distinguish on their own.

In this paper we present a procedure for the marking estimation of a Time Petri net system in the presence of unobservable (silent) transitions. Starting from the State Class Graph presented by Berthomieu and Diaz, we introduce a new graph called Modified State Class Graph that gives a representation of the evolution of the timed system. Then, we present a procedure that, given a timed observation, i.e., a sequence of observable transitions with their firing time instants, and a time instant τ, allows one to determine in which markings the system can be at time τ by solving a certain number of linear programming problems.

This paper presents a survey and evaluation of the efficiency of polynomial diagnosability algorithms for systems modeled by Petri nets and automata. A modified verification algorithm that reduces the state space by exploiting symmetry and abstracting unobservable transitions is also proposed. We show the importance of minimal explanations on the performance of diagnosability verifiers. Different verifiers are compared in terms of state space and elapsed time. It is shown that the minimal explanation notion involved in the modified basis reachability graph, a graph presented by Cabasino et al. [3] for diagnosability analysis of Petri nets, has great impact also on automata-based diagnosability methods. The evaluation often shows improved computation times of a factor 1000 or more when the concept of minimal explanation is included in the computation.

In this paper, we propose a logic-based Benders decomposition (LBBD), as well as an LBBD/gossip method to solve the heterogeneous multi-vehicle routing problem (HMVRP). HMVRP is a newly formalized extension of the NP-hard multi-traveling salesman problem (mTSP). First, a hybrid algorithm based on LBBD is formulated that decomposes the HMVRP into an assignment problem and a cluster of sequencing problems. The former is solved by a mixed integer linear programming (MILP) solver, and the latter by a dedicated TSP solver. Then, a gossip algorithm is constructed which utilizes the mentioned LBBD for local optimization to achieve better computational efficiency. The use of LBBD remarkably reduces the CPU time. Furthurmore, integrating the three layers of gossip algorithm, LBBD and the TSP solver, results in a very efficient solution method.

This paper demonstrates the application of Infinitesimal Perturbation Analysis (IPA) to performance optimization of fluid marked graphs. Recent developments in the theory of stochastic hybrid systems concern IPA techniques for gradient estimation of performance functions defined on Petri nets and their use in sample-path optimization. This paper takes a first step towards eventual applications in manufacturing by considering an example of workload balancing in a marked graph. In particular, it addresses the problem of balancing parts' inventories and product backorders in a production-system's model by controlling the parts' inflow rates. The paper defines the problem, describes the algorithm, and presents simulation results. Although the considered system is simple it captures the salient features of our approach, and the simulation results suggest its potential viability in future applications.

In this paper we consider marking estimation in labeled Petri nets whose initial marking is known to belong to a given convex set. We allow for silent transitions (i.e., transitions labeled with the empty word) and indistinguishable transitions (i.e., transitions sharing the same label with other transitions). We demonstrate that all sets of markings consistent with a given sequence of observations can be described in linear algebraic terms (as a union of convex sets) and a marking observer may be constructed offline under appropriate bounded ness assumptions. This reduces the problem of computing the set of markings consistent with a given observation sequence to the problem of moving along a path in a labeled directed graph.

In this paper, we propose an approach to the diagnosis of Petri nets in a decentralized setting that combines the decentralized scheme for automata presented by Debouk with the diagnosis approach for Petri nets based on the notion of basis markings and justifications presented by some of the authors of this paper. The decentralized architecture that we use is composed of a set of sites communicating their diagnosis information with a coordinator that is responsible for detecting the occurrence of failures in the system. In particular, we define three protocols that differ in the amount of information exchanged between the local sites and the coordinator and the rules adopted by the coordinator to compute the global diagnosis states. Finally, we prove that, as in the case of automata, diagnosability is strictly related to the presence of failure ambiguous strings.

A commonplace assumption in the fault diagnosis of discrete event systems (DESs) is that of modeling faulty events with unobservable transitions, i.e., transitions whose occurrence does not produce any observable label. The diagnostic system must thus infer the occurrence of a fault from the observed behavior corresponding to the firing of nonfaulty transitions. The presence of nonfaulty unobservable transitions is a source of additional complexity in the diagnostic procedure. In this paper, we assume that fault events can also be modeled by observable transitions, i.e., transitions whose occurrence produces an observable label. This does not mean, however, that the occurrence of such a transition can be unambiguously detected: In fact, the same label may be shared with other fault transitions (e.g., belonging to different fault classes) or with other nonfaulty transitions. We generalize to this new setting our previous results on the diagnosis of DESs using Petri nets based on the notions of minimal explanations and basis markings. The presented procedure does not require the enumeration of the complete reachability set but only of the subset of basis markings, thus reducing the computational complexity of solving a diagnosis problem.

In this paper we deal with the problem of designing an observer for Petri nets under the assumption that all transitions may be observed but there exist some uncertainties in the initial marking. In particular, the information on the initial marking is given in terms of fuzzy markings by associating a discrete membership function with each place. Some ideas on how to extend the proposed approach to the case of unobservable transitions are also discussed.

When discrete-event systems are used to model systems with a large number of possible (reachable) states, many problems such as simulation, optimization, and control, may become computationally prohibitive because they require some enumeration of such states. A common way to effectively address this issue is fluidization. The goal of this paper is that of studying the effect of fluidization on fault diagnosis. In particular, we focus on the purely logic Petri net (PN) model that results in the untimed continuous PN model after fluidization. In accordance to most of the literature on discrete-event systems, we define three diagnosis states, namelyN,U, andF, corresponding respectively to no fault, uncertain, and fault state. We prove that, given an observation, the resulting diagnosis state can be computed solving linear programming problems rather than integer programming problems as in the discrete case. The main advantage of fluidization is that it enables to deal with much more general PN structures. In particular, the unobservable subnet needs not be acyclic as in the discrete case. Moreover, the compact representation of the set of consistent markings using convex polytopes can be seen in some cases as an improvement in terms of computational complexity.

This paper deals with fault detection of manufacturing systems modeled by Petri nets. We show that the theoretical results obtained for continuous Petri nets allow us to treat with systems that are intractable using the theory developed for discrete Petri nets. In particular systems in which the unobservable part contains cycles can be studied. On the other hand, only three diagnosis states can be defined making impossible the splitting of the uncertain state into two different states, to obtain different degrees alarm for the uncertainty.

In this paper we consider a software tool for the simulation and analysis of discrete, continuous and hybrid Petri nets, called HYPENS. It is an open source tool we have recently developed in Matlab. The main contribution of this paper is that of demonstrating the efficiency of HYPENS via real several non trivial examples. In particular, we consider a family of purely discrete event systems modeling a queueing network, and a job shop system with finite capacity buffers and unreliable multi-class machines. A detailed analysis of the computational times and of the accuracy of the results is proposed. In particular, in the first case example, that is modeled using discrete Petri nets, the correctness of the results is proved using well known analytical results from the queueing theory.

In this paper, we deal with the problem of modeling railway networks with Petri nets so as to apply the theory of supervisory control for discrete event systems to automatically design the system controller. We provide a modular representation of railway networks in terms of stations and tracks including sensors and semaphores. We first ensure safeness and local liveness imposing both generalized mutual exclusion constraints and constraints also involving the firing vector. The detailed model used in this first step can be abstracted, considering a higher level description of a railway network that belongs to the class of ES PR (extended simple sequential process with resources) nets and show that global liveness may be enforced by adding appropriate monitor places designed using siphon analysis. In our approach, this can be done without an exhaustive computation of all siphons and we can characterize the cases in which the procedure can be recursively applied, giving a simple test for closed-loop net to remain an ES PR net.

In this paper we deal with the problem of determining a set of decentralized controllers for P/T nets that are able to impose a given global specification on the net behaviour. More precisely, both the global specification and the decentralized specifications are given in terms of generalized mutual exclusion constraints (GMECs) thus the controllers take the form of monitor places. In this paper we provide some preliminary results that are a first step towards a more general and systematic approach to the problem. The lines of our future research in this topic are described in details in the last section, devoted to conclusions and future works

In this paper we consider a quantized discrete-time linear quadratic regulator (DLQR) problem, namely a DLQR problem where the input u may only take values in a given finite set 14. Eased on our previous results on the optimal control of hybrid systems we show that the optimal control law for the quantized DLQR problem takes the form of a feedback control law, that can be obtained from a partition of the state space C, computed off-line. The numerical simulations carried out enabled us to observe a particular structure of C, related to the solution of the non-quantized DLQR problem. The lines of our future research in this topic are described in details in the last section, devoted to conclusions and future work

In this paper we deal with the problem of estimating the marking of a labeled Petri net with nondeterministic transitions. In particular, we consider the case in which nondeterminism is due to the presence of transitions that share the same label and that can be simultaneously enabled. Under the assumption that: the structure of the net is known, the initial marking is known, the transition labels can be observed, the nondeterministic transitions are contact-free, we present a technique for characterizing the set of markings that are consistent with the actual observation. More precisely, we show that the set of markings consistent with an observed word can be represented by a linear system with a fixed structure that does not depend on the length of the observed word.

a generalized mutual exclusion constraint (GMEC) is a linear constraint that limits the weighted sum of tokens in a subset of places of a place/transition net system. The corresponding controller takes the simple form of a monitor place that can be added to the net to obtain the closed-loop system. In this paper we extend this approach to the case of colored Petri nets, showing that a colored GMEC can express a set of linear constraints and can be enforced by a colored monitor place. We also develop a matrix representation of multisets that is useful for the design of the monitor place.

The real-time traffic control of railway networks authorizes movements of the trains and imposes safety constraints. The paper deals with the real time traffic control focusing on deadlock prevention problem. Colored Petri nets are used to model the dynamics of the railway network system: places represent tracks and stations, tokens are trains. The prevention policy is expressed by a set of linear inequality constraints, called colored Generalized Mutual Exclusion Constraints that are enforced by adding appropriate monitor places. Using digraph tools, deadlock situations are characterized and a strategy is established to define off-line a set of Generalized Mutual Exclusion Constraints that prevent deadlock. An example shows in detail the design of the proposed control logic.

Discusses the problem of controlling a Petri net whose marking cannot be measured but is estimated using an observer. The control objective is that of enforcing a set of generalized mutual exclusion constraints (GMEC) and all transitions are assumed to be controllable. The use of marking estimates (as opposed to the exact knowledge of the actual marking of the plant) leads to a worse performance of the closed-loop system and it may also be the case that, as a result of this, the controlled system reaches a deadlock. We present a general approach, based on siphon analysis, to recover from such an "observer induced" deadlock. The most interesting feature of our approach is that the observer, controller and deadlock recovery algorithms are all based on the same linear algebraic techniques, thus allowing the overall problem to be solved using a single formalism.

We deal with the problem of allocating a given number of tokens, so as to maximize the firing rate of a cyclic event graph with deterministic transition firing delays. We propose an incremental algorithm that is inspired by the algorithm formulated by Panayiotou and Cassandras (1999) for the case of kanban systems. The algorithm can be applied to a special class of nets in which tokens are allocated to places that belong to only one circuit: this class is powerful enough to model kanban systems. We provide necessary and sufficient conditions for the convergence to the optimum also in the case of multiple solutions.

A lumped-parameter model is considered for open-channel networks that expresses the dynamic relationship, in terms of state space variables, between gate opening sections and stored water volume variations in the different canal reaches with respect to a reference configuration of uniform flow. A procedure is suggested to approximate a real steady flow condition with an ideal uniform flow configuration. A decentralized control is obtained by determining the state feedback gain matrix, whose structure is imposed to be diagonal, that minimizes the H/sub 2/ norm of a suitable transfer matrix. A numerical validation of the linear model used to synthesize the control law is proposed. A comparison between the behaviour of the linear model and that of the non-linear unsteady one, whose evolution has been determined using the SIC software, is proposed.