无界Petri网的可达树的综述

Petri网自提出以来得到了学术界和工业界的广泛关注. Petri网系统的可达性是最基本性质之一.系统的其他相关性质都可以通过可达性进行分析.利用等价的有限可达树来研究无界Petri网可达性,依然是一个开放性问题.该研究可以追溯到40年前,但由于问题本身的复杂性和难度太大,直到最近20年,经过国内外诸多学者的不懈努力,才逐渐取得了一些阶段性的成果和部分突破.本文回顾了近40年来国内外学者为彻底解决该问题作出的贡献.重点对4种开创性的研究成果展开讨论,分别为有限可达树、扩展可达树、改进可达树及新型改进可达树.探讨了今后无界Petri网可达性问题的研究方向.     

Hierarchical Reachability Graph Generation for Petri Nets

Reachability analysis is the most general approach to the analysis of Petri nets. Due to the well-known problem of state-space explosion, generation of the reachability set and reachability graph with the known approaches often becomes intractable even for moderately sized nets. This paper presents a new method to generate and represent the reachability set and reachability graph of large Petri nets in a compositional and hierarchical way. The representation is related to previously known Kronecker-based representations, and contains the complete information about reachable markings and possible transitions. Consequently, all properties that it is possible for the reachability graph to decide can be decided using the Kronecker representation. The central idea of the new technique is a divide and conquer approach. Based on net-level results, nets are decomposed, and reachability graphs for parts are generated and combined. The whole approach can be realized in a completely automated way and has been integrated in a Petri net-based analysis tool.     

基于Petri网的可达树与可达图的构造与算法实现

Petri网是一种系统设计和分析的工具，为了完成Petri网的各项分析，还需要借助如可达树、可达图等工具。讨论了Petri网可达树与可达图的构造方法，并给出了相应的算法。     

时间约束Petri网的可达性分析研究

时间约束Ｐｅｔｒｉ风是具有广义时间约束的一类Ｐｅｔｒｉ网。目前有关ＴＣＰＮ状态可达性的研究仅局限于一些较简单的网,本文通过对ＴＣＰＮ的进一步研究,给出了更一般的状态可达性分析方法,并讨论了一般拓扑结构ＴＣＰＮ的可调度分析。     

时间约束Petri网的状态可达及可调度分析算法

时间约束Petri网是具有广义时间约束的一类Petri网。时间约束的引入使TCPN’s的演化与系统每一时刻的状态密切相关,导致网的动态复杂性。目前有关TCPN’s状态可达性的研究仅局限于一些较简单的网,该文通过对TCPN’s的进一步研究,给出了更一般的可达性分析方法及变迁可调度决策算法,并讨论了含冲突结构的TCPN’s的可调度分析。     

A Sufficient Condition for Reachability in a General Petri Net

Necessary and sufficient conditions for reachability exist only for special classes of Petri nets, acyclic Petri nets being one among them. We present a net transformation procedure that converts a general Petri net into an acyclic Petri net to utilize the available sufficient condition. We show the relationship between the reachable markings of the original Petri net and the associated acyclic Petri net. Given a firing count vector, we discuss how the sufficient condition for reachability in an acyclic Petri net could be utilized for a general Petri net. We also discuss the utility of the acyclic transformed net in determining the transition firing sequences of the reachable markings with known firing count vectors.     

时间Petri网的ECS-class可达性分析方法

时间Petri网(TPNs)是实时系统时间特性常用的描述和验证的Petri网模型,可达性分析是Petri网模型最基本分析方法.基于"状态类(State-class)"的可达性分析方法不能正确计算并发情况下的时间延迟,而基于"带时间戳的状态类(CS-class)"的可达性分析方法不能正确处理冲突情况下的事件调度,因此提出了"扩展的带时间戳的状态类(ECS-class)"可达性分析方法.它不仅正确的计算时间延迟,而且合理地调度事件.并对一个时间Petri网模型进行可达性分析验证.     

区间速率连续Petri网可达稳态必要性分析

文章就区间速率连续Petri网可达稳态的必要性问题进行研究,在介绍区间速率连续Petri网及其使能、引发语义的基础上首先给出区间速率连续Petri网在指定标识下具有稳态的条件;其次通过提出区间速率连续Petri网一种标识向量等价类划分方法从而给出分析区间速率连续Petri网可达稳态必要性的有效方法;最后给出一个应用例子,考察区间速率连续Petri网的可达稳态问题。     

Control of Safe Ordinary Petri Nets Using Unfolding

In this paper we deal with the problem of controlling a safe place/transition net so as to avoid a set of forbidden markings . We say that a given set of markings has property REACH if it is closed under the reachability operator. We assume that all transitions of the net are controllable and that the set of forbidden markings has the property REACH. The technique of unfolding is used to design a maximally permissive supervisor to solve this control problem. The supervisor takes the form of a set of control places to be added to the unfolding of the original net. The approach is also extended to the problem of preventing a larger set of impending forbidden marking. This is a superset of the forbidden markings that also includes all those markings from which—unless the supervisor blocks the plant—a marking in is inevitably reached in a finite number of steps. Finally, we consider the particular case in which the control objective is that of designing a maximally permissive supervisor for deadlock avoidance and we show that in this particular case our procedure can be efficiently implemented by means of linear algebraic techniques. Submitted to Discrete Event Dynamic Systems. A preliminary version of this paper titled “Control of safe ordinary Petri nets with marking specifications using unfolding,” was published in the Proc. IFAC WODES'04: 7th Work. on Discrete Event Systems (Reims, France), September 2004. Contact author is Alessandro Giua.     

时间Petri网弱语义模型的形式化分析

时间Petri网存在强语义和弱语义两种模型,弱语义模型更适合建模和分析外部环境触发的冲突选择问题,但其形式语义和可达性分析方面的研究,却很少有人问津。利用带标号的变迁系统定义时间Petri网弱语义模型的形式语义,采用时间戳状态类方法分析它的可达性,并证明了可达性问题的可判性和状态类时间戳的全局时间性质。     

软件编程构造和实现Petri Nets可达树

采用数据结构的思想和一些算法,将C 中的一些优良特性应用到Matlab编程语言中,用Matlab编程语言编程实现了PetriNets的可达树的构造。该程序对Petri Nets系统的动态性能分析具有一定的参考价值。     

Hybrid Petri Nets for Modeling and Analysis of Microgrid Systems

Hybrid Petri nets (HPNs) are widely used to describe and analyze various industrial hybrid systems that have both discrete-event and continuous discrete-time behaviors. Recently, many researchers attempt to utilize them to characterize power and energy systems. This work proposes to adopt an HPN to model and analyze a microgrid that consists of green energy sources. A reachability graph for such a model is generated and used to analyze the system properties.      

基于Petri网可达分析的代码搜索方法

复用已有高质量源代码可提高软件开发效率及软件质量.当前,基于用户提供的输入/输出对的匹配判断是代码语义搜索的主要方法之一,但该方法难以刻画完整代码行为,且仅能处理单输入类型.提出一种针对多种形式类型匹配的代码语义搜索方法.首先将代码集内各个代码片段中数据对象个数及类型的加工过程转换为Petri网模型;其次根据用户查询中...     

基于结构无竞争Petri网的DEDS的状态可达性可控性及其控制

本文给出了依靠代数递推计算判断结构无竞争Ｐｅｔｒｉ网的状态可达性的一种方法；提出了动态子网的概念，提高了判断速度；研究了结构无竞争Ｐｅｔｒｉ网的可达状态控制问题，给出了控制序列的设计方法。     

Synthesis of deadlock prevention policy using Petri nets reachability graph technique

This paper proposes a subclass of generalized stochastic Petri net (GSPN) model, called TS³PR, which is modified the systems of simple sequential processes with resources (S³PR) with timed information. Based on the subclass of GSPN, a new deadlock prevention policy is developed by using reachability graph technique. The foundation of the new control policy is to manipulate all the dead states of the system nets. This study is able to change dead states into vanishing ones by additional immediate transitions. A live TS³PR model can then be obtained. It is worthwhile to notice that this study is different from adding additional control place policies in previous literature. Experimental results, indicate that our new control policy is with maximally permissive markings than conventional place‐control ones. As a result, we can infer that our proposed control policy seems to be used in Petri nets deadlocked systems. To our knowledge, this is the first work that employs the additional transitions to obtain the deadlock prevention policy. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Detecting Data-flow Errors Based on Petri Nets With Data Operations

In order to guarantee the correctness of business processes, not only control-flow errors but also data-flow errors should be considered. The control-flow errors mainly focus on deadlock, livelock, soundness, and so on. However, there are not too many methods for detecting data-flow errors. This paper defines Petri nets with data operations (PN-DO) that can model the operations on data such as read, write and delete. Based on PN-DO, we define some data-flow errors in this paper. We construct a reachability graph with data operations for each PN-DO, and then propose a method to reduce the reachability graph. Based on the reduced reachability graph, data-flow errors can be detected rapidly. A case study is given to illustrate the effectiveness of our methods.      

Structuring Acyclic Petri Nets for Reachability Analysis and Control

The incidence matrices—from places to transitions and vice versa—of an acyclic Petri net can obtain a block-triangular structure by reordering their rows and columns. This allows the efficient solution of some reachability problems for acyclic Petri nets. This result is further used in supervisory control of Petri nets; supervisors for Petri nets with uncontrollable transitions are constructed by extending the method of Yamalidou et al. (1996) to Petri nets where transitions can be executed simultaneously. A large class of Petri nets with uncontrollable transitions is given for which the maximally permissive supervisor can be realized by a Petri net. The original specification is algorithmically transformed—by using the results for acyclic Petri nets—into a new specification to take the presence of uncontrollable transitions into account. The supervisor is obtained by simple matrix multiplications and no linear integer programs need to be solved. Furthermore, a class of Petri nets is given for which the supervisor can be realized by extending the enabling rule with OR-logic.     

基于混合Petri网的一类混合系统的动态分析

利用混合Ｐｅｔｒｉ网对一类典型的混合系统－－模式切换系统进行建模和分析；提出模式切换系统动态平稳性的概念；给出了二模式切换系统的平稳条件以及求解平稳点的算法，并用实例进行了说明。     

基于随机对象Petri网的柔性制造系统性能分析

为了增强传统对象Petri网的定量分析能力,提出随机对象Petri网模型。该模型具备随机性和层次特性,获得与随机Petri网的等价关系,从宏观和微观2个层面对系统进行性能分析,并将该模型应用到柔性制造系统中。实验结果表明,该系统保留了面向对象的建模能力,具有较强的定量分析能力。