Modeling and stability analysis of hybrid dynamical systems based on extended differential Petri nets

In this paper, extended differential Petri nets (EDPNs), a new extension of differential Petri nets (DPNs), is proposed. Compared with the existing extension of DPNs, EDPNs has two improvements: (1) the restriction on the enabling condition that depends on the weight of arc is relaxed, i.e., allow the enabling condition has more general form; (2) the definition is extended for the weight of arc. By these two improvements, EDPNs presents larger flexibility and modeling power than the existing extension of DPNs. Using this model, the stability of hybrid dynamical systems (HDS) is studied. A new Lyapunov’s stability theorem of HDS is given. Furthermore, by using the information of index matrix and a new composite energy function, the stability theorem of linear HDS is obtained.     

Modeling uncertainty reasoning with possibilistic Petri nets

Manipulation of perceptions is a remarkable human capability in a wide variety of physical and mental tasks under fuzzy or uncertain surroundings. Possibilistic reasoning can be treated as a mechanism that mimics human inference mechanisms with uncertain information. Petri nets are a graphical and mathematical modeling tool with powerful modeling and analytical ability. The focus of this paper is on the integration of Petri nets with possibilistic reasoning to reap the benefits of both formalisms. This integration leads to a possibilistic Petri nets model (PPN) with the following features. A possibilistic token carries information to describe an object and its corresponding possibility and necessity measures. Possibilistic transitions are classified into four types: inference transitions, duplication transitions, aggregation transitions, and aggregation-duplication transitions. A reasoning algorithm, based on possibilistic Petri nets, is also presented to improve the efficiency of possibilistic reasoning and an example related to diagnosis of cracks in reinforced concrete structures is used to illustrate the proposed approach.     

模糊Petri网与遗传算法相结合的优化策略

如何确定模糊产生式规则的各项参数对模糊Petri网(FPN)的建立具有非常重要的意义,一直是尚未解决的难题。文中首次将遗传算法引入到模糊Petri网的参数寻优过程,提出了一种基于遗传算法的参数寻优算法,该算法实现不依赖于经验数据,对初始输入无严格要求。仿真实例表明,由此训练出的参数正确率较高,所得的FPN具有很强的泛化能力和自适应功能。     

生化网络的随机Petri网建模与分析

细胞的行为是随机性的,学习细胞中的随机性有助于理解细胞的组织,设计和进化。建立、确认和分析随机的生化网络模型是当前计算系统生物学领域的一个重要研究主题。当前,标准的Petri网模型已经成为生化网络模拟和定性分析的有力工具。尝试使用随机Petri网对生化网络进行建模与分析,简单描述了随机Petri网理论对标准Petri网的扩充,通过对二聚作用和肌动蛋白这两个典型例子的建模与演化模拟,介绍、论证了随机Petri网理论的新应用。     

Modeling and generating context-aware agent-based applications with amended colored Petri nets

Context-awareness is become more crucial in mobile distributed computing systems. However, sophisticated modeling methods to analyze context-aware systems are still very few. Among those, the Colored Petri Net (CPN) is promising because it is proven to be useful for modeling system dynamics and concurrency control in more efficient ways. However, to support managing multiple configurations of components of context-aware applications, some features need to be added to specialize the CPNs. To address these challenges, our research has two idea: (a) to decompose a system into several meaningful subsystems, each of which we will call a pattern, and (b) to separate context from the patterns to realize context-pattern independence. Hence, we propose a modeling methodology to represent and analyze a context-aware agent-based system, which tends to be highly complex. We introduce CPNs as a method of capturing the dynamics of this contextual change. We define CPNs and a way to apply them in context-aware agent-based systems. We also describe a prototype system that we have developed called CPN Generator, which translates CPN specification into Java programs.     

Modeling and online scheduling of flexible manufacturing systemsusing stochastic Petri nets

The authors discuss the modeling of flexible manufacturing systems (FMSs) under uncertainty and evaluate a rule base for online scheduling. To represent uncertain events in an FMS, such as failure of machine tools, repair time, and processing time, they develop continuous-time and discrete-time stochastic Petri nets with hierarchical structures for constructing the FMS model. For obtaining an efficient schedule for the FMS with an online real-time basis, they construct a rule base and evaluate its performance using the FMS simulation system proposed     

Modeling and analysis of timed Petri nets using heaps of pieces

The authors show that safe timed Petri nets can be represented by special automata over the (max, +) semiring, which compute the height of heaps of pieces. This extends to the timed case the classical representation a la Mazurkiewicz of the behavior of safe Petri nets by trace monoids and trace languages. For a subclass including all safe free-choice Petri nets, we obtain reduced heap realizations using structural properties of the net (covering by safe state machine components). The authors illustrate the heap-based modeling by the typical case of safe jobshops. For a periodic schedule, the authors obtain a heap-based throughput formula, which is simpler to compute than its traditional timed event graph version, particularly if one is interested in the successive evaluation of a large number of possible schedules     

Modeling and scheduling of ratio-driven FMS using unfolding time Petri nets

In this paper, we focus on the analysis of a cyclic schedule for the determination of the optimal cycle time and minimization of the Work in Process (WIP for short). Especially, this paper deals with product ratio-driven FMS cyclic scheduling problem with each other products and ratios using Timed Petri nets unfolding (TPN for short). TPN slicing and unfolding are applied to analyze this FMS model. We can divide original system into subsystem using TPN slices and change iterated cycle module into acyclic module without any loss of other behavior properties.     

Modeling and analysis of a mail processing plant using Petri nets

This article outlines the utilization of Petri nets as a computerized process modeling and analysis tool for the study of the Edmonton Mail Processing Plant (MPP). Development of new systems or designing improvement in existing system—such as the MPP—are some of the challenges faced by decision makers and managers on a regular basis in the industry. In order to make prudent decisions, modeling and analysis of the underlying processes that constitute new or existing systems has become essential. Usually process modeling and analysis is performed by initially developing a graphical portrayal of the process and then by dynamically studying the response of the process to external and internal factors. In this article an overview of Petri net based process modeling and analysis is provided. Petri net is a formal graphical modeling tool that can be efficiently utilized as a process modeling and analysis tool because it can graphically portray and dynamically simulate a process in an integrated manner. The objective of this article is to highlight the symbolic graphic format and dynamic simulation capabilities of Petri nets. The article contributes significantly in the area of computer based decision making and provides value to practicing engineers and project managers who manage complex tasks.     

基于Petri网的工作流模式建模及应用

工作流模式建模是工作流模型的基础,Petri网同步器是目前最有效的工作流模型建模方法。使用网和同步距离对工作流模式进行分析,将目前常用的工作流模式归纳成为三种：完全同步、竞争同步、非同步。而Petri网同步器只能表示完全同步,不能表示竞争同步和非同步,为此提出一种改进的同步器,通过改进同步类型,使得同步器可以建模三种同步模式,较之改进前的同步器,增强了建模竞争同步模式和非同步模式的能力。     

基于Gillespie算法的生化随机Petri网演化分析

Petri网既有严格的数学表达方式,又有直观的图形描述形式,是当前生物化学系统模拟和定性分析的一个有力工具。作为标准Petri网的一个重要扩展,随机Petri网使得可以定量地分析生物化学系统。建立了两个典型的生物化学系统的随机Petri网模型：Schlogl系统和转录调控系统,并使用Gillespie随机仿真算法模拟了这些生化随机Petri网模型的状态演化。     

基于着色Petri网的联合反导作战系统建模

防空反导作战系统是一个复杂的军事系统,具有同步、并发、冲突等特点。应用着色Petri网技术对联合反TBM作战系统进行建模,符合联合反导作战系统的特点,能够有效地分析联合反导作战系统的静态结构和动态行为。分析了联合反导作战系统的信息交换关系,建立了系统的CPN模型,对模型进行了验证和仿真。     

基于增广混合Petri网的CPS事件建模

信息物理融合系统是一类将信息系统和物理系统连接并融合在一起的混合系统,包含了感知、通信、计算与控制等多种技术,其系统操作既包括离散的计算过程,又包括连续的物理过程。针对此特性,提出一种以事件为驱动、以数据为核心的增广混合Petri网模型。首先,CPS具有事件驱动的内在属性,为事件定义1个用于赋予数据值的变量因子,以数据作为事件执行程度的核心;其次在混合Petri网的基础上加入时间和空间属性,以及为变迁的发生引入条件弧概念;最后,通过对自适应巡航控制系统的运行机理进行建模分析,验证了所提出模型的可行性。     

基于CPN的发布/订阅系统的建模及分析

提出了一种基于着色Petri网(CPN)的pub/sub系统协议分析方法.基于一种结构化P2P网络上的pub/sub系统协议,用着色Petri网对事件发布的消息处理进行建模和描述,并利用CPN tools对模型进行模拟仿真,通过对模型的可达图进行分析,表明了协议具有活性、可达性和有界性,验证了协议的可用性.     

Numerical solution of nonlinear elliptic partial differential equations by a generalized conjugate gradient method

We have studied previously a generalized conjugate gradient method for solving sparse positive-definite systems of linear equations arising from the discretization of elliptic partial-differential boundary-value problems. Here, extensions to the nonlinear case are considered. We split the original discretized operator into the sum of two operators, one of which corresponds to a more easily solvable system of equations, and accelerate the associated iteration based on this splitting by (nonlinear) conjugate gradients. The behavior of the method is illustrated for the minimal surface equation with splittings corresponding to nonlinear SSOR, to approximate factorization of the Jacobian matrix, and to elliptic operators suitable for use with fast direct methods. The results of numerical experiments are given as well for a mildy nonlinear example, for which, in the corresponding linear case, the finite termination property of the conjugate gradient algorithm is crucial.     

基于CPN的列控系统等级转换建模与分析

在高速列车运行过程中,列控系统等级转换过程所用的时长和转换成功概率,直接影响列车运行安全和行车效率。利用有色Petri网对CTCS-3级列控系统和CTCS-2级列控系统之间等级转换以及典型设备故障导致降级场景分别建模,模拟等级转换过程中RBC（Radio Block Center,无线闭塞中心）,车载设备,有源应答器之间的信息交互过程。分析了列车速度对等级转换实时性的要求和对转换成功概率的影响,以及突发降级的可能性,结果表明建模方法满足CTCS-3级列控系统的安全性和兼容性要求。