Original Petri Nets Research Articles

Quotient Petri nets*

This work introduces the concepts of quotient Petri net (QPN) and dual quotient Petri net (DQPN) as tools to build abstractions of Petri net (PN) structures with three different purposes: a) to have an abstraction (dynamic congruence) of a PN, b) to obtain distributed representations of systems; c) to remove undesired system dynamics. The main advantages are: a) QPN and DQPN preserve sufficient information of the original PN enabling engineers to implement hierarchical or distributed controllers, observers, diagnosers, etc. schemes avoiding/reducing centralized coordinators, b) QPN and DQPN can be efficiently computed by using linear transformations. In fact, a method for computing QPNs and DQPNs is introduced. This work introduces a methodology to compute QPNs and DQPNs that preserve the consistent and conservative from the original PNs.

A decomposition algorithm of Petri net utilizing index function

Recently, it is difficult to simulate, analyze and control a real knowledge-based system using the correspondence Petri net (PN) when there exist many current states. To overcome the state explosion problem of PN, an efficient decomposition algorithm is presented to divide a large-scale PN into a series of corresponding sub-PNs by keeping the consistency of dynamic properties. In this novel decomposition approach, an index function is defined to judge the subnet needs to be decomposed or not. Furthermore, an exhaustive analysis on the consistency of related dynamic properties is also discussed between the original PN and the corresponding sub-PNs. Finally, a case study is carried out to illustrate the feasibility and validity of the proposed approach.

Petri Net controller synthesis based on decomposed manufacturing models

Utilizing of supervisory control theory on the real systems in many modeling tools such as Petri Net (PN) becomes challenging in recent years due to the significant states in the automata models or uncontrollable events. The uncontrollable events initiate the forbidden states which might be removed by employing some linear constraints. Although there are many methods which have been proposed to reduce these constraints, enforcing them to a large-scale system is very difficult and complicated. This paper proposes a new method for controller synthesis based on PN modeling. In this approach, the original PN model is broken down into some smaller models in which the computational cost reduces significantly. Using this method, it is easy to reduce and enforce the constraints to a Petri net model. The appropriate results of our proposed method on the PN models denote worthy controller synthesis for the large scale systems.

One-Step Control-Ahead Approach for the Design of an Optimal Petri-Net Based Deadlock Prevention Policy

This paper focuses on establishing a Petri net (PN)-based deadlock prevention policy for large-scale systems whose state spaces are prone to the explosion problem phenomenon. When using the reachability analysis technique, the main burden is that the number of states grows exponentially with respect to the PN structure and, thereby, synthesizing a lively controlled Petri net model (PNM) becomes an extremely complex procedure. The proposed method reduces the initial marking of the PNM to reduce the size of the reachability graph. Such a reachability graph is reduced exponentially and the activity places are derived iteratively using a well-established invariant-based control method. When the PNM becomes live, the control places are integrated to the original PNM and, therefore, the advantage of this method lies in that the control of the original PN model starts at an earlier stage, i.e., before enumerating the full reachability graph and which we call it one-step control-ahead of a PNM. Compared with the existing methods, the new method requires the control of a very small-sized reachability graph and, therefore, it is convenient for large-scale and bounded PNs. Two examples are used to illustrate the proposed approach. Experimental results show that we can obtain optimal supervisors for the net models.

Simultaneous Reduction of Petri Nets and Linear Constraints for Efficient Supervisor Synthesis

Due to state-space explosion and uncontrollable events in discrete-event systems, it is very difficult to design supervisors to enforce user-defined linear-constraints and ensure the liveness of their Petri-net (PN) models with complex structures. Different from all the existing methods, which are to transform original constraints into admissible or weakly admissible ones, the method proposed in this work aims to reduce linear-constraints and PN models simultaneously. As a result, an original PN control problem is equivalently reduced to a simpler one, i.e., the optimal supervisors for them make the same restriction on the behavior of a discrete-event system. Moreover, it can be guaranteed that the original PN system is live if and only if the reduced one is so. Since the state space of a PN may grow exponentially with its size, and the sizes of real discrete-event systems are often too large to handle, the proposed method is useful to greatly reduce the computational complexity of both property-analysis and supervisor-synthesis of discrete-event systems.

Property preserving operation for simplifying Petri nets with inhibitor arcs

Petri nets' simplification of property preservation is a significant approach for Petri nets analysis.Meanwhile,the computational ability of Petri nets with inhibitor arcs is equal to Turing machine.From the perspective of series transition and series places respectively,this paper proposed two simplified methods of the Petri nets with inhibitor arcs.Finally,it proved that the characteristics such as aliveness,boundedness and weak fairness of simplified Petri nets with inhibitor arcs were kept unanimous with the original Petri nets with inhibitor arcs by these methods.

Confusion Diagnosis and Control of Discrete Event Systems Using Synchronized Petri Nets

AbstractThe mixture of conflicting transitions and concurrent transitions in Petri nets can lead to the loss of conflict information, which is an unfortunate phenomenon in discrete event systems, usually called confusions. They appear in the processes of resource allocation and may cause incomplete decision‐making on conflicts. Hence, a confusion detection method and a control strategy are required. This paper proposes a class of confusion control event reconfigurable (CCR) nets to control confusions with the evolution of markings. Their properties such as safety and liveness with the mapping from original Petri nets to CCR nets are investigated. Two confusion control algorithms are proposed to generate a set of control code sequences, which can completely control the occurrences of confusions. Then, a confusion detection algorithm with polynomial time complexity is developed. Finally, an example of confusion analysis in automated manufacturing systems is presented.

A hybrid approach to design deadlock-free Petri net controller for discrete event systems

The issue of supervisory control of discrete event systems (DES) based on Petri nets (PN) has been investigated by using various methods. However, there exists a problem that the supervisor, introduced to enforce the given specification, causes a deadlock in the closed-loop system, especially when the deadlock occurs in the closed-loop system in which the original plant model is live. To address this problem, we propose a hybrid approach to design a deadlock-free PN controller for DES with given specification. The approach mainly consists of two stages. Firstly, a supervisor is designed to enforce the given specification using the reported place invariants method. Then, we regard the obtained closed-loop system with deadlock introduced by the supervisor as a new plant net and adopt the theory of regions to design a deadlock-free PN controller. The controller designed by our approach is guaranteed to be maximally permissive when the original plant PN is fully controllable and observable. Even for partially controllable and observable plant PN, it is possible to obtain a suboptimal solution.

Discrete, Continuous and Hybrid Petri Nets (David, R. and Alla, H.; 2004)

This text provides the unifying perspective for all of the predominant variations of the Petri net (PN) modeling framework while highlighting the differentiating elements among them and the implied relationships. The book also fills a gap in the existing PN literature on continuous and hybrid PNs. Some of the topics covered include: an introduction to basic concepts appearing in the original PN modeling framework of autonomous and ordinary PNs; a more formal characterization of the autonomous ordinary PN model; nonautonomous PNs; autonomous continuous and hybrid PNs; and timed dynamics in continuous and hybrid PNs. The book is supported with 15 appendices treating topics that include regular expressions and languages, conflict resolution, elements of graph theory, Grafcet, the linearity of the fundamental equation for continuous PNs, the graphs of relations among conflicts, and piecewise constant maximal firing speeds.

Petri Net Models for Assembly Sequences Planning

Assembly sequences can be represented by a Petri net(PN) which characterizes dynamic system changes and provides a tool for obtaining optimal assembly sequences. In this study some assembly operation constraints are considered in order to obtain more practical sequences which are conformed to real situations. In order to enhancing the efficiency of the assembly sequence planning, knowledge-based Petri net, combining an usual Petri net with expert’s knowledge and experiences, is proposed to construct the assembly model. With the complexity of the product, the product’s assembly model size will be too large to analysis. So the basic subnets are used to reduce the large PN. And the reduced version can be used for the analysis of the original PN. To verify the validity and efficiency of the approach, a variety of assemblies including some complicated products from industry are tested, and the corresponding results are also presented.

Verification of bounded Petri nets using integer programming

Model checking based on the causal partial order semantics of Petri nets is an approach widely applied to cope with the state space explosion problem. One of the ways to exploit such a semantics is to consider (finite prefixes of) net unfoldings--themselves a class of acyclic Petri nets--which contain enough information, albeit implicit, to reason about the reachable markings of the original Petri nets. In [19], a verification technique for net unfoldings was proposed, in which deadlock detection was reduced to a mixed integer linear programming problem. In this paper, we present a further development of this approach. The essence of the proposed modifications is to transfer the information about causality and conflicts between the events involved in an unfolding, into a relationship between the corresponding integer variables in the system of linear constraints. Moreover, we present some problem-specific optimisation rules, reducing the search space. To solve other verification problems, such as mutual exclusion or marking reachability and coverability, we adopt Contejean and Devie's algorithm for solving systems of linear constraints over the natural numbers domain and refine it, by taking advantage of the specific properties of systems of linear constraints to be solved. Another contribution of this paper is a method of re-formulating some problems specified in terms of Petri nets as problems defined for their unfoldings. Using this method, we obtain a memory efficient translation of a deadlock detection problem for a safe Petri net into an LP problem. We also propose an on-the-fly deadlock detection method. Experimental results demonstrate that the resulting algorithms can achieve significant speedups.

Les réseaux de Petri pour le contrôle des systèmes à événements discrets

In this thesis, we propose two control synthesis methods for discrete event systems (DES) modeled by Petri nets (PN) and having some uncontrollable transitions. The first approach allows to design a PN model of the controlled system by adding a set of control places to an original PN. The controlled model has to achieve a desired behavior corresponding to the so-called forbidden state transition problem (FSTP). The controller designed by this approach is maximally permissive. Further desired behaviors that can't be realized by PN based controller are well characterized. The second control synthesis approach we propose in this thesis addresses the particular case of forbidden state problem of marked graphs. The control decision can be taken on-line by evaluating simple predicates at each current marking.

Tutorial and Survey Articles: An introduction to Petri Nets

This paper describes the fundamental concepts and characteristics of Petri nets (PNs) that make them a significant tool for modeling and analyzing asynchronous systems with concurrent and parallel activities and follows the extensions that improved the implementation capabilities of the original PNs. Their first and most relevant extension was time modeling, a vital aspect of system performances not considered in the original version. There are several possibilities for introducing time in PNs. Among them, a technique that associates time with places is presented in some detail. As PNs tend to become cumbersome and time consuming when large and complex systems are involved, a method for decomposing timed PNs of open queuing networks is reviewed here. Though initially developed as an information/computer-based technique, PNs were immediately adopted in a variety of application areas, such as manufacturing, design, planning and control. Viewed through a more recently developed programming perspective, the ordinary PNs became “high level” PNs suitable for defining different data types and for applying hierarchical approaches. It is expected that the robust theoretical basis of this tool coupled with its visual and flexibility features will continue to appeal to researchers and practitioners alike in a variety of domains and as a result will continue to evolve and expand.

On supervisory policies that enforce liveness in completely controlled Petri nets with directed cut-places and cut-transitions

The process of synthesizing a supervisory policy that enforces liveness in a Petri net (PN), where each transition can be prevented from firing by an external agent, can be computationally burdensome in general. We consider PNs that have a directed cut place or a cut-transition. A place (transition) in a connected PN is said to be a cut place (cut-transition) if its removal will result in two disconnected component PNs. A cut place is said to be a directed cut-place, if in the original PN, all arcs into this cut place emanate from transitions in only one of the two disconnected component PNs. The authors show there is a supervisory policy that enforces liveness in the original PN if and only if similar policies exist for two PNs derived from the disconnected components obtained after the removal of the directed cut-place (cut-transition). The utility of this observation in alleviating the computational burden of policy synthesis is illustrated via example.

Deadlock prevention using Petri nets and their unfoldings

Unfoldings of Petri nets (PN) provide a method for the analysis of concurrent systems without restoring the state space of a system. This allows one to overcome the “state explosion” problem. Many properties of the initial PN (boundedness, safety, persistency and hazards) can be checked by constructing the unfolding. A deadlock prevention procedure first detects deadlocks using an unfolding. Then, the first method reduces the unfolding to a set of deadlock-free subunfoldings that cover all live behaviours. The second method uses a direct transformation at the level of the original PN. The methods are implemented as subroutines in the Berkeley program SIS. Although the deadlock detection problem is known to be NP-complete, experimental results show that for highly parallel specifications deadlock prevention by unfoldings is typically more efficient than deadlock prevention based on symbolic BDD (binary decision diagrams) traversal of the corresponding reachability graph.

Inverse petri nets: properties and applications

On the foundation of basic Petri net theory, the paper proposes the definitions of Inverse Petri Nets, discusses the relations of inverse petri nets and its original petri nets, proves the theorem of transition enablity and the full - ref lection theorem, and outlines the applications of inverse petri nets. We find that the inverse Petri nets are a promising tool for deeling with some application problems. Using the concept of inverse Petri nets and analysis methodology of reachability, it is easy to solve the design problems of initial state and input sequences in discrete event control systems. The concept of inverse Petri nets is meaningful for constructing the Petri net models of describing logic proof problems.