A vector Lyapunov function approach for the stabilization of discrete event systems

State-Partition-Based Control of Discrete Event Systems for Enforcement of Regular Language Specifications

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

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.

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.

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.

Petri net models are used to detect and isolate faults in case of discrete event systems as manufacturing, robotic, communication and transportation systems. This chapter addresses two problems. The first one is the structure designs and parameters identification of the Petri net models according to the observation and analysis of the sequences of events that are collected. Deterministic and stochastic time Petri nets are concerned. The proposed method is based on a statistical analysis of data and has a practical interest as long as sequences of events are already saved by supervision systems. The second problem concerns the use of the resulting Petri net models to detect, isolate and characterize faults in discrete event systems. This contribution includes the characterization of intermittent faults. This issue is important because faults are often progressive from intermittent to definitive and early faults detection and isolation improve productivity and save money and resources.

Petrinets are the suitable tool for modeling and analysis of discrete event systems. The effective methods of analyzing the discrete event systems (DES) are exhibited by Petri nets. The entire structure of the system is mathematically expressed using Petrinets and also all the properties are analysed by different methods. The properties of Petrinets are different in various systems, a Flexible Manufacturing System (FMS) requires production activities in which raw materials, energy, labour, and equipment are combined together in the modification process for the production of good quality goods.” The word “flexible” explains the capability of the system to relate productively to make changes in the system. These changes can be internal failure of the system or classification problems such as a sample or external changes in the structure of the model as well as demand for the process. The inherent limitations such as undecidable properties, complexity in checking, automatic verification of the modeled system are existing in FMS. This paper explains a study on FMS using Petri net reduction. A PN underlies event structures with casuality and compatibility relations. Partial order methods and reduction methods reduce the complexity of constructing the reachability graph. The determination of PN system through reduction methods in recent years focused by many researchers. The significance of reduction methods are highlighted to execute the faster analysis of a system. Instead of coverability trees and the graphical representation the incidence matrix of the PNs are used for the reduction methods. Reduction methods are used to simplify large scale PNs into “equivalent” smaller nets. Boundedness, liveness, simplification of implicit places, shared resources and elimination of self-loops are checked though equivalent smaller nets. The structure of FMS is preserved.

This paper is about the incremental computation of control sequences for discrete event systems in uncertain environments where uncontrollable events may occur. Timed Petri nets are used for this purpose. The aim is to drive the marking of the net from an initial value to a reference one, in minimal or near-minimal time, by avoiding forbidden markings, deadlocks, and dead branches. The approach is similar to model predictive control with a finite set of control actions. At each step only a small area of the reachability graph is explored: this leads to a reasonable computational complexity. The robustness of the resulting trajectory is also evaluated according to a risk probability. A sufficient condition is provided to compute robust trajectories. The proposed results are applicable to a large class of discrete event systems, in particular in the domains of flexible manufacturing. However, they are also applicable to other domains as communication, computer science, transportation, and traffic as long as the considered systems admit Petri Nets (PNs) models. They are suitable for dynamical deadlock-free scheduling and reconfiguration problems in uncertain environments.

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

Presently, the number, types, and distribution of resources in a resource allocation system (RAS), may change frequently and dynamically due to fluctuant customer demands. Such changes in a resource allocation (RA) specification mean different production or service behaviors yielded by the providers. This new situation gives rise to a challenging problem, namely, how to switch smoothly the provider systems to support different production. This paper tries to address this problem from the viewpoint of discrete event system (DES) supervisory control. A Petri net (PN) controller of an RAS can be designed from a resource allocation specification using P-invariant. Once the RA specification is changed, the controller is updated following it. Moreover, if the changed specification is unreasonable, the whole control system, are reconfigured to reach a legal system state and a newly reasonable resource allocation solution is re-calculated. Specifically, the paper proposed a reconfiguration method of a PN control system that is transformed into PN reachability analysis problem using a mathematic programming approach. In our method, not only the transition firing costs but also the steps of concurrent firing are taken into account to achieve an optimal reconfiguration solution. Finally, an example is provided for illustrating the application of the mentioned methods.

On fluidification of Petri Nets: from discrete to hybrid and continuous models

Residuals-based fault diagnosis of industrial automation systems using timed and untimed Interpreted Petri nets