Modelling and temporal performances evaluation of networked control systems using (max, +) algebra

In this paper, we address the problem of temporal performances evaluation of producer/consumer networked control systems. The aim is to develop a formal method for evaluating the response time of this type of control systems. Our approach consists on modelling, using Petri nets classes, the behaviour of the whole architecture including the switches that support multicast communications used by this protocol. (max, +) algebra formalism is then exploited to obtain analytical formulas of the response time and the maximal and minimal bounds. The main novelty is that our approach takes into account all delays experienced at the different stages of networked automation systems. Finally, we show how to apply the obtained results through an example of networked control system.     

基于赋时事件图的故障诊断

赋时事件图(TEG)是一类用于描述同步特性的重要的Petri网.本文提出并研究了基于赋时事件图的故障诊断问题.文中定义了两类系统故障类型:变迁失效(Invalidation)故障和变迁时间延迟(Time_lag)故障.基于事件图关联矩阵,通过研究变迁失效故障的可观测传播特性,引入了故障特征向量的概念.基于此,给出了失效故障的可诊断性的充分必要条件.对于时延故障,提出了一种基于变迁触发时间估计进行故障诊断的简单算法.并基于此算法,研究了时延故障的可诊断条件.     

State‐Feedback Control for a Class of Timed Petri Nets Subject to Marking Constraints

The paper contributes with an original method of designing a control for discrete event systems modeled by a class of timed Petri nets. Precisely, this work deals with the closed loop control of Timed Event Graphs (TEGs) under specifications expressed with linear marking constraints. The objective of the controller is to limit the number of tokens in some places of these TEGs. The behavior of TEGs is represented by a system of difference equations that are linear in Min‐Plus algebra and the constraints are described by a set of inequalities, which are also linear in Min‐Plus algebra. A formal approach to design control laws that guarantee compliance with these marking constraints is proposed. For this, two sufficient conditions for the existence of control laws are proposed. The computed controls are causal feedbacks, which can be represented by a set of marked and timed places. The proposed method is illustrated in two applications: a manufacturing production line and an assembly system.     

Feedback control for a class of discrete event systems with critical time

This paper presents an algebraic approach for control laws synthesis of timed event graphs subjected to strict temporal constraints. This class of discrete event systems is deterministic, in the sense that its behaviour only depends on the initial marking and on the control that is applied. This behaviour can be modelled by a linear equations system in Min-Plus algebra. The temporal constraint is represented by an inequality that is also linear in the Min-Plus algebra. Then, a method for the synthesis of control laws ensuring the respect of constraints is described. We give explicit formulas characterising a control law, which ensures the validity of the temporal constraints. It is a causal feedback control, involving delays. The method is illustrated on an example.     

基于事件代数的入侵检测系统

该文提出了一种基于事件代数的多事件入侵特征的形式化定义机制,用一组事件运算来表示入侵特征,对多事件入侵检测特征定义中的若干普遍问题给出了系统化的解决方案。文章还提出了一种“带约束的有色Petri网模型”来构造事件检测引擎。     

Control of a class of discrete event systems with disturbances and capacity constraints: Application to a disassembly problem

This study proposes an analytical control method for the meeting of capacity constraints in discrete event systems with disturbances. More precisely, it consists of computing control laws for partially controllable and observable timed event graphs that are subject to marking constraints. To resolve the issue, linear Min-Plus models are used to describe the behavior of these graphs, and the constraints are expressed by inequalities in Min-Plus algebra. Sufficient conditions for the existence of causal control laws to guarantee marking specifications are established. Finally, to illustrate the efficiency of the proposed approaches in this paper, an application for a disassembly process with some disturbance inputs and limited component capacities is carried out.     

实时并发离散事件系统的监控

用受控赋时Ｐｅｔｒｉ网为具有并发事件的实时离散事件系统建模，并研究了这类模型下的监控问题，给出了实现给定并发事件语言的监控器存在的充要条件和一种动态监控方法。     

Parametric Transformation of Timed Weighted Marked Graphs: Applications in Optimal Resource Allocation

Timed weighted marked graphs are a subclass of timed Petri nets that have wide applications in the control and performance analysis of flexible manufacturing systems.Due to the existence of multiplicities(i.e.,weights)on edges,the performance analysis and resource optimization of such graphs represent a challenging problem.In this paper,we develop an approach to transform a timed weighted marked graph whose initial marking is not given,into an equivalent parametric timed marked graph where the edges have unitary weights.In order to explore an optimal resource allocation policy for a system,an analytical method is developed for the resource optimization of timed weighted marked graphs by studying an equivalent net.Finally,we apply the proposed method to a flexible manufacturing system and compare the results with a previous heuristic approach.Simulation analysis shows that the developed approach is superior to the heuristic approach.     

进路建立过程的时间有色petri网建模与仿真

计算机联锁软件作为计算机联锁系统的核心主控软件,可靠性和安全性需建立在好的安全模型之上,提出了采用时间有色Petri网对进路建立的具体过程进行形式化建模,时间戳可以得知联锁设备的精确动作时刻以及操作持续时间,通过CPN Tools进行编辑和仿真,以VC++6.0为开发环境完成代码编写进行验证,体现时间有色Petri网描述联锁系统逻辑和性能特性的特点,以便在软件开发初期尽早发现系统的设计错误或缺陷,突出采用时间有色Petri网建模的可靠性和安全性。     

Control of Petri nets subject to strict temporal constraints using Max-Plus algebra

In this paper, we treat the control problem of timed discrete event systems under temporal constraints. This type of constraint is very frequent in production systems, transportation network and in networked automation systems. Precisely, we are interested in the validation of strict temporal constraints imposed on the paths in a timed event graph (TEG) by using Max-Plus algebra. Not all the transitions of the considered TEG model are controllable, i.e. only the input transitions are controllable. An analytical approach for computing state feedback controllers is developed. Sufficient condition is given for the existence of causal control laws satisfying the temporal constraints. In the first, a TEG with observable transitions is considered. Then, the proposed approach is extended to the partially observable TEG. The synthesised feedback can be interpreted by places of control connected to the TEG to guarantee the respect of the time constraints. The proposed method is illustrated in the assembly system example.     

基于Petri网的工作流过程模型及资源分布分析

针对工作流系统的特点对时延Petri网模型进行扩展,提出了一种新的工作流建模方法,即扩展时延Petri网。给出了扩展时延Petri网的定义,并用该方法分析了工作流四种基本模型;给出了利用排队论和随机Petri网理论计算工作流模型时间性能指标的新方法,用这种方法可求得与实例到达率相关的工作流模型平均完成时间。最后应用上述方法讨论了工作流资源分布的几种模式,并与模拟结果加以对比,计算结果的最大误差在3%左右,说明基于扩展时延Petri网的方法是分析工作流系统时间性能的有效方法。     

Invariants of Timed Petri Nets

A linear fundamental equation for a timed Petri net is constructed. Full and partial invariants of state and behavior of a timed Petri net are introduced. Properties of invariant nets are analyzed. Interrelations of full and partial invariants are shown. Examples of analysis of net models of production systems and processes are described.     

基于Petri net建模的资源调度的蚁群算法

利用了受控赋时Petri net建立了分布式系统中的资源调度的模型,并应用仿真器进行了仿真。由于在进行大规模的模型分析时,不适合采用仿真器来模拟,因而引进了蚁群算法来优化模型,可以得到较好的结果。     

一种随机Petri网模拟系统时延分析的新方法*

本文首先引入了时延网和闭网的概念,证明了Petri网N为时延网的充要条件是其闭网为常返网;然后,从时延网模型出发,讨论了变迁发射时间为任意分布的随机离散事件系统时延特性的求取方法,给出了时延密度的计算公式。     

加权的时间Petri网工作流模型研究

时间性能分析是工作流模型分析和评价的重要方面。介绍了Petri网和工作流网的基本概念,提出了加权时间扩展工作流网,对加权时间扩展工作流网的基本组件进行了时间分析,给出了平均时间的计算方法。通过网上订购商品和生产车间工作流模型,利用基本组件的时间性能分析方法,对这两个工作流模型进行了时间性能分析。     

Modeling and control of drug assignment for pharmaceutical cabinets using discrete event systems approaches

The public health sector, considered to be vital, especially in this pandemic crisis of COVID-19, requires automation and control of drug distribution in pharmacies commonly called: “Dispensing.” In this paper, we address the medication assignment problem for automated dispensing cabinets (ADCs). First, we use a network of conflicting timed event graphs (CTEGs), a class of timed Petri nets with shared resources, to model pharmaceutical cabinets. Second, we develop a new method for controlling CTEGs under mutual exclusion constraints (MECs) to solve the problem of drug assignment, using a control approach based on Min-Plus algebra. Finally, a case study of assigning drugs is given to illustrate the proposed methodology and show the efficiency of the developed control laws.     

Refinement of Actions in a Real-Time Process Algebra with a True Concurrency Model

In this paper, we develop techniques of action refinement in a real-time process algebra that allows urgent interactions to model timeout. Semantic counterpart is carried out in a real-time non-interleaving causality based setting, timed bundle event structures. We show that our refinement notions have the following nice properties: the observable behaviour of the refined system can be inferred compositionally from the observable behaviour of the original system and from the observable behaviour of the processes substituted for the actions; the timed extensions of observational pomset trace equivalence and observational history preserving bisimulation equivalence are both congruences under our refinement; and the syntactic and semantic refinements coincide up to the aforementioned equivalence relations with respect to a cpo-based denotational semantics.     

基于Petri网的公文管理工作流模型

该文针对现有的工作流模型在实际应用中有时难以全面描述整个应用系统这一问题,结合公文管理工作流的实际应用环境,提出了一个相对完整的基于Petri网的工作流模型,并给出了该模型的正确性验证。