The Complexity of Diagnosability and Opacity Verification for Petri Nets

This paper addresses the problem of current-state opacity of discrete event systems (DES) modeled with Petri nets. A system is said to be current-state opaque if the intruder who only has partial observations on the system's behavior is never able to infer that the current state of the system is within a set of secret states. Based on the notion of basis markings, an efficient approach to verifying current-state opacity in bounded Petri nets is proposed, without computing the whole reachability set or exhaustively enumerating the set of markings consistent with the observation. An example showing the efficiency of the approach is presented.

In this paper a hybrid approach is proposed for supervisory control of discrete event systems (DES) subject to forbidden states. Assuming that an uncontrolled bounded Petri net (PN) model of a (plant) DES and a set of forbidden state specifications are given, the proposed approach computes a maximally permissive and nonblocking closed-loop hybrid model. The first step is to simplify the given PN model by means of PN reduction rules. The simplified model and the specifications are then represented as buffers, and supervisory control theory (SCT) is applied to obtain a Ramadge–Wonham (RW) supervisor in the form of an automaton. After reduction of the latter’s state size by a ‘control congruence’, the simplified RW supervisor is represented by a so-called auto-net and coupled to the given uncontrolled PN plant model by means of inhibitor arcs to represent the disabling actions. The plant model and supervisor auto-net run concurrently, synchronizing on shared events. This procedure provides a maximally permissive and nonblocking ‘hybrid’ (mixed PN/automaton) closed-loop controlled system. The method is straightforward logically, graphically, and technologically. Its applicability is shown by two examples, one of them a workcell from the PN control literature.

Individuals, populations and fluid approximations: A Petri net based perspective

This paper presents an approach to perform Activity Based Costing (ABC) with Petri nets. ABC is a powerful methodology to calculate various of discrete event systems (e.g. production systems). Petri net models of discrete event systems are easy to create, comprehend, and to perform analysis, the mathematics behind Petri nets is also easy to grasp. This paper shows how ABC can be performed with Petri nets, so that various involved in a discrete event system can be easily measured with the help of the Petri net model. After a short introduction to ABC and Petri nets, this paper shows the approach which basically embeds various cost drivers as firing costs and firing times of transitions in a Petri net model. This work also presents a case study that is done with GPenSIM, a toolbox realized with this approach.

Traffic lights are commonly used in the intersection in urban areas nowadays. In fact a network of the traffic lights regulating the urban vehicle can be viewed as a complex discrete-event system (DES). It is proved that Petri nets are one of the methodologies for modeling, analyzing and controlling on DES. A new approach via programmable logic controller (PLC) and Petri net synthesis is proposed in this paper. Firstly, we described the typical urban traffic lights control using Petri nets. Having compared with three methods for Petri nets realization, the best implementation method of the traffic lights control system was one which made with the PLC. The sequential function chart (SFC) of the PLC system is also given in the thesis. The result shown that the method has many advantages at improving flexibility and troubleshoots of system and reducing the difficulty in its realization.

Discrete event systems in applications, such as industry and supply chain, may show a very complex behavior. For this reason, their design and operation may be carried out by the application of optimization techniques for decision making in order to obtain their highest performance. In a general approach, it is possible to implement these optimization techniques by means of the simulation of a Petri net model, which may require an intensive use of computational resources. One key factor in the computational cost of simulation‐based optimization is the size of the model of the system; hence, it may be useful to apply techniques to reduce it. This paper analyzes the relationship between two Petri net formalisms, currently used in the design of discrete event systems, where it is usual to count on a set of alternative structural configurations. These formalisms are a particular type of parametric Petri nets, called compound Petri nets, and a set of alternative Petri nets. The development of equivalent models under these formalisms and the formal proof of this equivalence are the main topics of the paper. The basis for this formal approach is the graph of reachable markings, a powerful tool able to represent the behavior of a discrete event system and, hence, to show the equivalence between two different Petri net models. One immediate application of this equivalence is the substitution of a large model of a system by a more compact one, whose simulation may be less demanding in the use of computational resources.

Event Structures for Local Traces

This work presents a framework for the coordination control of Discrete Event Systems (DES) based on Petri Nets (PN). The concept of enabling arcs is used in the transitions for signal reception by the controller. The structural properties of the PN controller are studied by analyzing it as an interpreted PN. PN models of both the controller and the system to be controlled are presented, the latter performed through a Temporized Petri Net (TPN). A software module for DES coordination control was developed, based on the above cited structure and programmed in C-language which interacts with the DES local controllers. This program is run in an IBM-compatible 486 PC.KeywordsDiscrete event systemscoordination controlPetri nets.

The work undertaken in this thesis is about the integration of two well-known methodologies: Petri net (PN) model Ii ng/analysis of industrial production processes and Artificial Intelligence (AI) optimisation search techniques. The objective of this integration is to demonstrate its potential in solving a difficult and widely studied problem, the scheduling of Flexible Manufacturing Systems (FIVIS). This work builds on existing results that clearly show the convenience of PNs as a modelling tool for FIVIS. It addresses the problem of the integration of PN and Al based search methods. Whilst this is recognised as a potentially important approach to the scheduling of FIVIS there is a lack of any clear evidence that practical systems might be built. This thesis presents a novel scheduling methodology that takes forward the current state of the art in the area by: Firstly presenting a novel modelling procedure based on a new class of PN (cb-NETS) and a language to define the essential features of basic FIVIS, demonstrating that the inclusion of high level FIVIS constraints is straight forward. Secondly, we demonstrate that PN analysis is useful in reducing search complexity and presents two main results: a novel heuristic function based on PN analysis that is more efficient than existing methods and a novel reachability scheme that avoids futile exploration of candidate schedules. Thirdly a novel scheduling algorithm that overcomes the efficiency drawbacks of previous algorithms is presented. This algorithm satisfactorily overcomes the complexity issue while achieving very promising results in terms of optimality. Finally, this thesis presents a novel hybrid scheduler that demonstrates the convenience of the use of PN as a representation paradigm to support hybridisation between traditional OR methods, Al systematic search and stochastic optimisation algorithms. Initial results show that the approach is promising.

The use of shared resources is a major problem occurring in discrete event (DE) systems, including manufacturing systems, computer systems, communication systems, highway/vehicle systems, and others. The issues involve problems of assignment of resources when the same resources are simultaneously requested by more than one job. Failure to suitably assign, or dispatch, resources in such situations can have serious deleterious effects on system performance, resulting in extreme cases in system deadlock [7]. Computer operating systems engineers and industrial engineers have used the concepts of circular wait (CW) and circular blocking in analysis of such phenomena [41, 24]. Various concepts in Petri nets (PN) are extremely useful for dealing with deadlock and a great deal of research has been done from the PN point of view (see references, especially [11, 14, 19]). The PN approaches are often based on the notion of the siphon, which indeed is called a “deadlock” in some works [26]. Unfortunately, it is known that many problems in scheduling, dispatching, and deadlock analysis are NP-hard [12], so that significant increases in computing power do not significantly improve computational ability. Neither PN nor CW approaches have addressed this issue.

Solving the deadlocks avoidance problem in Resource Allocation Systems (RAS) in Discrete-Event Systems (DES) is a rife problem, especially in Flexible Manufacturing Systems (FMS), alias Automated Manufacturing Systems (AMS). Petri Nets (PN) are an effectual tool often used at this procedure. In principle, there are two basic approaches how to deal with deadlocks in RAS based on PN. They are listed and illustrated here. First of the approaches is realized by means of the supervisor based on P-invariants of PN, while the second one is realized by means of the supervisor based on PN siphons. While the first approach needs to know the reachability graph/tree (RG/RT) expressing the causality of the development of the PN model of RAS, in order to find (after its thorough analysis) the deadlocks, the second approach needs the thorough analysis of the PN model structure by means of finding siphons and traps. Next, both approaches will be applied on the same PN model of RAS and the effectiveness of the achievement of their results will be compared and evaluated. Several simple illustrative examples will be introduced. For the in-depth analysis of the problem of deadlock avoiding, next Part 2 of this paper is prepared, where the newest research will be introduced and illustrated on more complicated examples. If necessary (because of the limited length of particular papers), also the third part – Part 3, will be prepared.

This paper is concerned with fault detection and location of discrete event systems (DES) modeled using interpreted Petri nets (IPN). The approach held deals with IPN models in which the marking is partially known. A diagnosis scheme that tracks the DES inputs and outputs is proposed; it allows detecting and locating an unexpected behavior within the DES. The diagnoser handles a monitoring model, expressed also as an IPN, which is computed from the DES model through an induced conservative marking law.

Many technological, industrial or economical systems are described by discrete event system (DES) models. The decision making processes that arise in the design and operation of this kind of systems can be afforded by means of algorithmic methodologies. A large range of approaches based on the simulation of the behavior of the system have been reported to answer this problem. Their main advantage consists of being applicable to most of the systems. An important drawback is the significant computational resources required to perform an exhaustive exploration of the state space due to the combinatorial explosion. A manual choice of a reduced set of configurations to be simulated can be improved by the use of parametric Petri nets and a metaheuristic search of the most promising ones. In this paper, a review of some definitions of parametric Petri net found in the literature is presented, as well as a definition for the general framework of stating optimization problems of both, the operation and the design of the model of the DES. Moreover, a methodology to obtain such a parametric Petri net, called compound Petri net, from an easier-to-obtain set of alternative Petri nets is proposed and an application example is given.

Pascal’s triangle is a classical mathematical construct, historically studied for centuries, that organises binomial coefficients in a triangular array and serves as a cornerstone in combinatorics, algebra, and number theory. Herein, we propose to model it with Petri nets, a formal specification technique derived from discrete event systems. A minimal Petri net is created that generates Pascal’s triangle under a simple arithmetic rule. Token counts in each place coincide with binomial coefficients, providing a direct combinatorial interpretation. Two other classical structures emerge from this model: by colouring tokens depending on their parity, the Sierpiński triangle appears; by routing tokens randomly at each branching, the binomial distribution arises, converging to a Gaussian limit as depth increases. As a result, a single Petri construction unifies three mathematical objects: Pascal’s Triangle, Sierpiński’s Triangle, and the Gaussian distribution. This connection illustrates the invaluable potential of Petri nets as unifying tools for modelling discrete mathematical structures and beyond.

The cooperation of autonomous agents is synthesized in order to satisfy demands imposed on a group of agents or on MAS (multi agent systems). Petri nets (PNs), especially place/transition PNs (P/T PNs), are used for modelling the agents. The modular approach is utilized on that way. PN-based methods of discrete event systems (DES) control and supervising are utilized in order to synthesize the cooperation of the agents. The usefulness and applicability of the approach is demonstrated by examples and case studies.KeywordsAgentsbipartite graphscontrolcooperationdiscrete-event systemsPetri netssupervisorsynthesis