Petri网本原可重复向量的求解算法及实现

Petri网本原可重复向量是一个重要结构性质.本文定义了网N的可重复向量表出集pre-SPRV(N),证明一个网的本原可重复向量集是唯一的,并且给出它的一个求解算法.算法首先求出网N变迁扩充网的所有极小T-不变量,由此求得N的一个可重复向量表出集,然后依次考察其中的每一个向量,将其中的多余向量去掉,得出网N的本原可重复向量集.最后算法被实现并用于实例以展示算法性能,相关算法的程序实现可以作为已有Petri网分析工具的一个组件.     

一般网中结构公平的极小标识的求解算法

公平性(fairness)是Petri网的基本性质。在该文中利用网的关联矩阵求解出一般网中的基本可重复向量组,在其中找出该网的极小支集,并构造出该极小支集构的外延子网,然后利用文献[1]中给出的方式求解结构公平网的极小标识,得到了一个多项式时间算法。     

基于同步合成的结构复杂Petri网的行为描述

首先分析了一类结构简单的Petri网--S-网的语言性质,得到了它们的行为描述方法.拓展了Petri网同步合成的概念,证明了给定一个结构复杂的Petri网都可通过一组S-网的同步合成运算而得到,并给出了相应的求解算法.引入语言的同步交运算,分析了结构复杂的Petri网与其同步合成子网之间的行为关系,给出了结构复杂Petri网的行为描述算法,为利用网语言分析实际系统的行为特征提供了可靠的理论依据和方法.     

Petri网化简技术的动态特性研究

对于大而复杂的Petri网,“节点过多,状态爆炸”一直是阻碍其技术发展的主要问题,因此,如何有效地简化Petri网一直是Petri网研究领域的一个研究热点。将Petri网简化为若干子网是一个很有效的方法。提出了库所指标概念,根据该指标,给出了Petri网的分解定义,并给出了相关算法。在此基础上,依据所给出的算法研究化简技术的动态特性,将子网与原网的特性对应起来进行研究,为复杂系统的Petri网的分析提供了一种有效的途径。     

基于分解子网的Petri网不变量的分析

分析系统性能时,Petri网不变量具有重要意义。为了减小求解的计算复杂性,基于Petri网的分解,并利用关联矩阵的构成特点,分析总网和分解后子网的不变量之间的关系。对分解后的子网为一般Petri网,采用的连接为自环连接和同步连接的情形,得到了总网P/T-不变量可对分解保持的一些充分、必要或充要条件。     

Petri网分解的保性条件分析

Petri网的分解技术是用于复杂网系统分析的一种有效手段 .基于库所指标的 Petri网分解方法 ,将一个复杂的网系统分解成结构满足 |· t|≤且 |t· |≤ 1的简单子网 ,通过分解得到的子网与原系统的状态和行为之间存在着一种投影关系 .但是 ,子网本身也增加了一些不必要的状态和行为 (原网系统在子网上的投影只是子网状态和行为的一个子集 ) .本文提出分解过程中的状态保性和行为保性的概念 ,证明了分解过程中行为和状态保性的充要条件 ,基于标识可达图给出了相应的判定算法 ,对复杂系统的 Petri网分析方法提供了更为有效的理论和可行的技术     

基于库所指标分解的Petri网结构性质分析

Petri网的分解技术是复杂网系统分析的一种重要手段,基于库所指标的分解方法将系统分解为一组S-网。基于库所指标的分解方法来分析原网的结构性质,得到了原网对子网结构性质的保持关系,并给出了几种通过子网直接判定原网结构性质的方法,为结构复杂Petri网的性质分析提供了有效的方法。     

基于变迁指标分解的Petri网性质分析

Petri网的分解技术是复杂网系统分析的一种重要手段,基于变迁指标的分解方法将系统分解为一组T-网。通过获得分解子网的结构性质以及子网与原网间的性质保持关系,得到了判定原网结构性质的一些方法和结论;同时给出了判定原网系统活性的一个条件。所得结果为结构复杂Petri网的性质分析提供了有效的方法。     

基于分解的连续Petri网性质分析方法

讨论了最大速度恒定连续Petri网（CCPN）的分解方法以及如何通过子网分析得到原网的性质。首先给出基于库所归属的分解方法,实现了CCPN的分解。为了保证通过子网分析原网的正确性,对合成网的动态不变性进行了证明,并证明了CCPN子网结构性质与原CCPN网性质的对应关系。最后以实例验证了通过子网分析原网的正确性。     

基于库所指标的Petri网分解方法

一、引言 Petri网是系统模拟和分析的有效工具。对于一个规模较大的网系统,由于变迁和库所数目的增多,其分析显得比较麻烦。针对这个问题,国内外的许多学者作了大量的工作,他们提出了网化简、网运算,定义了化简子网、逐次化简以及针对特殊子网、特殊结构的化简方法。文[6]和文[7]分别给出了网系统的“和分解”和“并分解”方法,并讨论了通过这两种分解方法得到的子网同原网在结构性质方面的对应关系。本文通过指定库所集的指标函数,给出一种基于库所指标集的Petri网分解方法,通过分解得到结构简单的子网系统:|t|≤1且|t|≤1,原系统的状态和语言与子系统之间存在着一种投影关系,通过子网间的同步合成可得到原系统的状态和行为,对用Petri网分析大规模系统提供了一种有效的方法。由于篇幅所限,本文没有介绍Petri网的基本概念和术     

自动制造系统Petri网的公平活性控制策略

基于Petri网的不变式理论,针对典型的自动制造系统,提出了Petri模型强制公平性 和活性的方法.首先,基于网论T-不变式的概念,把系统的网模型设计为一个公平网.此后,利 用P-不变式把一个公平网设计为一个活的且公平网.同时,提出了非冗余严格极小信标的概念, 大大简化了系统的分析与设计.一般说来,非冗余严格极小信标是系统严格极小信标一个小的 子集,尤其对于复杂系统的网模型.研究结果表明,只要使非冗余的严格极小信标受控,则系统 所有的严格极小信标就不会被清空.文中举例说明了这些控制方法的应用.研究结果适用于一 大类柔性制造系统,具有相当的普遍性.这种方法对于自动制造系统的调度设计也具有一定意义 和价值.     

Elementary siphons of Petri nets and their application to deadlock prevention in flexible manufacturing systems

A variety of important Petri net-based methods to prevent deadlocks arising in flexible manufacturing systems (FMS) are to add some control places and related arcs to strict minimal siphons (SMS) such that no siphon can be emptied. Since the number of minimal siphons grows in general exponentially with respect to a Petri net size, their disadvantages lie in that they often add too many additional places to the net, thereby making the resulting net model much more complex than the original one. This paper explores ways to minimize the new additions of places while achieving the same control purpose. It proposes for the first time the concept of elementary siphons that are a special class of siphons. The set of elementary siphons in a Petri net is generally a proper subset of the set of all SMS. Its smaller cardinality becomes evident in large Petri net models. This paper proves that by adding a control place for each elementary siphon to make sure that it is marked, deadlock can be successfully prevented. Compared with the existing methods, the new method requires a much smaller number of control places and, therefore, is suitable for large-scale Petri nets. An FMS example is used to illustrate the proposed concepts and policy, and show the significant advantage over the previous methods.     

Extended Elementary Siphons and Their Application to Liveness‐Enforcement of Generalized Petri Nets

As a significant structural object, siphons are extensively employed to implement a large number of deadlock prevention and liveness‐enforcing methods for flexible manufacturing systems modeled by Petri nets. By linear combinations, a set of elementary siphons is chosen from all strict minimal ones to be controlled and thus the structural complexity of a supervisor is greatly reduced. The concept of elementary siphons is originally proposed for ordinary Petri nets. When applied to generalized Petri nets, their selection and controllability require an additional study. In this work, the concept of augmented siphons is proposed to extend the application of the elementary ones to a class of generalized Petri nets, GLS³PR. Based on graph theory, a siphon extraction algorithm is developed to obtain all strict minimal siphons, from which augmented elementary ones are computed. In addition, the controllability conditions of dependent siphons are developed. Through fully investigating the net structure, especially weight information, the set of augmented elementary siphons is more compact and well suits for generalized Petri net models under consideration. Some examples are used to illustrate the proposed method.     

基于Petri网的柔性制造系统一种预防死锁方法

基于Petri网的结构特性分析,研究了FMS(柔性制造系统)一种预防死锁方法.提出了 Petri网的一种特殊拓扑结构--基本信标的概念.在Petri网中基本信标的集合是SMS(严格极 小信标)集合的一个真子集.尤其在大型Petri网系统中,基本信标的集合比SMS的集合要小得 多.对于Petri网的一个子类S3PR,只对每一个基本信标添加一个库所使其不被清空,就可实现 预防死锁,也就是说无须控制S3PR的所有SMS而达到无信标被清空的目的.此外,对于S3PR, 还提出了一种求取SMS和基本信标的方法.相对于现在普遍采用的控制所有SMS来预防死锁 的策略,其具三方面优势.1)只需控制少量的SMS即所谓的基本信标.相应地,添加少量的控制 库所和连接弧,就可得到无死锁或活的Petri网.2)不需要先行计算出极小信标的集合.3)明显 地,这种方法更适合大型Petri网系统.我们通过穿插在文中的一个例子来说明这些方法.     

Necessary and sufficient liveness condition of GS3PR Petri nets

Structural analysis is one of the most important and efficient methods to investigate the behaviour of Petri nets. Liveness is a significant behavioural property of Petri nets. Siphons, as structural objects of a Petri net, are closely related to its liveness. Many deadlock control policies for flexible manufacturing systems (FMS) modelled by Petri nets are implemented via siphon control. Most of the existing methods design liveness-enforcing supervisors by adding control places for siphons based on their controllability conditions. To compute a liveness-enforcing supervisor with as much as permissive behaviour, it is both theoretically and practically significant to find an exact controllability condition for siphons. However, the existing conditions, max, max′, and max″-controllability of siphons are all overly restrictive and generally sufficient only. This paper develops a new condition called max*-controllability of the siphons in generalised systems of simple sequential processes with resources (GS³PR), which are a net subclass that can model many real-world automated manufacturing systems. We show that a GS³PR is live if all its strict minimal siphons (SMS) are max*-controlled. Compared with the existing conditions, i.e., max-, max′-, and max″-controllability of siphons, max*-controllability of the SMS is not only sufficient but also necessary. An example is used to illustrate the proposed method.     

Enumeration algorithms for minimal siphons in Petri nets based on place constraints

The paper addresses the problem of enumerating minimal siphons in an ordinary Petri net. The algorithms developed in this work recursively use a problem partitioning procedure to reduce the original search problem to multiple simpler search subproblems. Each subproblem has specific additional place constraints with respect to the original problem. Some results on algorithm correctness, convergence, and computational complexity are provided, as well as an experimental evaluation of performance. The algorithms can be applied to enumerate minimal, place-minimal siphons, or even siphons that are minimal with respect to given subsets of places.     

A deadlock prevention approach for a class of timed Petri nets using elementary siphons

To solve the problem of deadlock prevention for timed Petri nets, an effective deadlock prevention policy based on elementary siphons is proposed in this paper. Without enumerating reachable markings, deadlock prevention is achieved by adding monitors for elementary siphons, increasing control depth variables when necessary, and removing implicit, liveness‐restricted and redundant control places. The final supervisor is live. First, a timed Petri net is stretched into a stretched Petri net (SPN). Unchanging the system performance, each transition in the SPN has a unit delay time. Then the siphon‐control‐based approach is applied. Monitors computed according to the marking constraints are added to the SPN model to ensure all strict minimal siphons in the net invariant‐controlled. A liveness‐enforcing supervisor with simple structure can be obtained by reverting the SPN into a TdPN. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

信标基底的可选择性在制造系统死锁控制中的应用

本文基于Petri网模型,讨论柔性制造系统的死锁控制问题.为了建立结构简单的Petri网控制器,本文在以前的工作中提出了信标基底的概念.信标基底是一组满足特定条件的严格极小信标集合.本文证明基于不同的信标基底,建立的受控系统其容许性能也不同.而容许性是评价死锁控制策略优劣的重要标准之一.故如何选择信标基底,提高受控系统的容许性能是值得研究的问题.本文讨论了使受控系统容许性能大大提高的信标基底的选择条件.基于该条件,为柔性制造系统建立有效的死锁控制策略.最后,通过两个例子解释该条件和策略.     

基于信标的柔性制造系统的优化死锁预防策略

针对柔性制造系统（FMS）中的死锁问题,根据矩阵理论给出了Petri网中基本信标的概念,进而提出一种基于基本信标和混合整数规划法（MIP）的死锁预防策略．该策略将最优基本信标作为控制对象,以混合整数规划法给出的系统无死锁条件为目标函数．不考虑从属信标受控条件便可在多项式时间内使系统受控．该控制策略的显著特点是以较低的计算复杂度实现整个系统受控,并使需要添加的控制库所和连接弧大大减少．控制实例证明了其有效性．     

An iterative method for synthesizing non-blocking supervisors for a class of generalized Petri nets using mathematical programming

This paper presents a novel and computational deadlock prevention policy for a class of generalized Petri nets, namely G-systems, which allows multiple resource acquisitions and flexible routings with machining, assembly and disassembly operations. In this research, a mixed integer programming (MIP)-based deadlock detection technique is used to find an insufficiently marked minimal siphon from a maximal deadly marked siphon for generalized Petri nets. In addition, two-stage control method is employed for deadlock prevention in Petri net model. Such proposed method is an iterative approach consisting of two stages. The first one is called siphons control, which adds a control place to the original net for each insufficiently marked minimal siphon. The objective is to prevent minimal siphons from being insufficiently marked. The second one, called control-induced siphons control, is to add a control place to the augmented net with its output arcs connecting to source transitions, which assures that there is no new insufficiently marked siphon generated due to the addition of the monitors. Compared with the existing approaches, the proposed deadlock prevention policy can usually lead to a non-blocking supervisor with more permissive behavior and high computational efficiency for a sizeable plant model due to avoiding complete siphon enumeration. Finally, a practical flexible manufacturing system (FMS) example is utilized to illustrate the proposed method.