Modeling and synthesis of supervisory control based on Petri nets for distributed objects. I. Interaction mechanism and the basic method

We describe a methodology of discrete event modeling for a class of distributed objects and their required behavior (specifications) for the design of real time automation systems. In our methodology, we use the structured discrete event system (SDES2) model: on the first stage, it is used to analyze the functionality and coherence of the object and its specification; on the second, we propose for SDES2 a basic synthesis method that works for the models of object and supervisor based on Petri nets (both modeling and controlling). At the same time, we propose to synthesize the supervisor as a Petri net embedded in SDES2 with a feedback circuit in order to restrict the object’s operation according to specification requirements. We propose an interaction mechanism for the modeling and controlling Petri nets with the object and the external environment. In essence, the interaction mechanism is an object control scheme based on the constructed net. This mechanism analyzes the current state of the object and computes the controls that should be passed on to the object’s actuators. Computations are done with a cyclic procedure looping over the matrix representation of the net.     

A Survey of Petri Net Methods for Controlled Discrete Event Systems

This paper surveys recent research on the application of Petri net models to the analysis and synthesis of controllers for discrete event systems. Petri nets have been used extensively in applications such as automated manufacturing, and there exists a large body of tools for qualitative and quantitative analysis of Petri nets. The goal of Petri net research in discrete event systems is to exploit the structural properties of Petri net models in computationally efficient algorithms for computing controls. We present an overview of the various models and problems formulated in the literature focusing on two particular models, the controlled Petri nets and the labeled nets. We describe two basic approaches for controller synthesis, based on state feedback and event feedback. We also discuss two efficient techniques for the on-line computation of the control law, namely the linear integer programming approach which takes advantage of the linear structure of the Petri net state transition equation, and path-based algorithms which take advantage of the graphical structure of Petri net models. Extensions to timed models are briefly described. The paper concludes with a discussion of directions for future research.     

Suboptimal time management of discrete event systems with uncontrollable events modeled by Petri nets

Preventing systems from entering to forbidden states is a crucial issue in discrete event systems control. Adding supervisors to the system is a common method to avoid entering to forbidden states. In discrete event systems modeled by Petri net adding a supervisor could be done by means of control places. Since, the time is not considered in designing this supervisor, in presence of uncontrollable transitions adding control places can lead to increase the operation time of the system modeled by timed Petri net. Because, the firing of some transitions is prevented when it is not necessary. So, to design a more efficient controller, we will be required to use time information of the system component. Therefore, in this paper, a method for optimizing the time behavior of a supervised timed Petri net will be proposed. To obtain an efficient operation, some timed places as timer will be added to the net. The time of this timer places is calculated to permit firing of some controllable transitions in order to enter into some weakly forbidden states while entering to forbidden states is prevented. This concept leads to increase the speed of system as well as obtain an acceptable operation. This method can be applied for all systems modeled by Petri nets. The efficiency of proposed approach will be discussed and validated with a case study.     

具有不可控变迁离散事件系统的Petri网控制器

考虑可用具有不可控变迁的受控Petri网建模的离散事件动态系统.提出了在这类系统中实现一组不等式约束的控制器的综合方法.所提出的控制器可通过给系统Petri网模型增加一些Petri网元素来实现,其计算是建立在本文提出的Petrl网的路增益概念基础上的.方法是系统、简单、计算量小.     

Petri net supervisors for DES with uncontrollable and unobservabletransitions

A supervisor synthesis technique for Petri net plants with uncontrollable and unobservable transitions, that enforces the conjunction of a set of linear inequalities on the reachable markings of the plant, is presented. The approach is based on the concept of Petri net place invariants. Each step of the procedure is illustrated through a running example involving the supervision of a robotic assembly cell. The controller is described by an auxiliary Petri net connected to the plant's transitions, providing a unified Petri net model of the closed-loop system. The synthesis technique is based on the concept of admissible constraints. Procedures are given for identifying all admissible linear constraints for a plant with uncontrollable and unobservable transitions, as well as methods for transforming inadmissible constraints into admissible ones. A technique is described for creating a modified Petri net controller that enforces the union of all of these control laws. The method is practical and computationally inexpensive in terms of size, design time, and implementation complexity     

On optimal supervisory control with trimness of controlled systems

In this paper, we propose a design algorithm for an optimal supervisor for guaranteeing the trimness of the controlled system. We generalize the earlier work of Kumar and Grag based on the induced flow network of a given discrete event system. Specifically, the proposed algorithm is directly applicable to a discrete event system and minimizes the net cost of the optimal supervisor, which ensures that the controlled system is a trim generator with a polynomial-order computational complexity.     

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。     

Control Synthesis of Petri Nets Based on S-Decreases

A method for constructing a controller for a discrete event system modeled by a Petri net is presented in this paper. The control specification of the system is given by a set of linear inequality constraints defined on the marking of the net. The controller that forces the net to obey the constraints is an extended Petri net, which is synthesized based on minimal support S-decreases. The method can deal with general Petri nets with uncontrollable transitions, and then provides a systematic way for synthesizing net-based controllers for discrete event systems.     

基于有限容量库所的离散事件系统的Petri网控制器综合——第1部分

针对由Petri网建模的离散事件系统, 提出了一种新的控制器设计方法. 控制器是基于有限容量库所的概念构造而成的, 并使被控对象在给定的一组线性不等式约束下运行, 而给定的线性不等式约束是定义在库所标识上的. 控制器的综合利用了有限容量库所Petri网转换为 (普通 )无限容量库所Petri网的技术. 针对约束的不同情况, 给出了相应的Petri网的控制器的设计方法.     

可视化分布组件协调环境

分布组件的协调是基于组件的分布系统开发中的一个基本问题。针对具体应用,提出了一种分布组件协调模型－－Ｃｏｎｃｅｒｔｏ。Ｃｏｎｃｅｒｔｏ模型以Ｐｅｔｒｉ网为理论基础,综合了现有的控制驱动和数据驱动两类协调模型。Ｐｅｔｒｉ网的变迁与分布组件系统中的事件、条件、操作和时间信息结合起来,提供了与计算机系统交互的方法。在Ｃｏｎｃｅｒｔｏ模型基础上,实现了可视化分布组件协调环境,对分布组件系统进行并发死锁验证     

SimQPN—A tool and methodology for analyzing queueing Petri net models by means of simulation

The queueing Petri net (QPN) paradigm provides a number of benefits over conventional modeling paradigms such as queueing networks and generalized stochastic Petri nets. Using queueing Petri nets (QPNs), one can integrate both hardware and software aspects of system behavior into the same model. This lends itself very well to modeling distributed component-based systems, such as modern e-business applications. However, currently available tools and techniques for QPN analysis suffer the state space explosion problem, imposing a limit on the size of the models that are tractable. In this paper, we present SimQPN—a simulation tool for QPNs that provides an alternative approach to analyze QPN models, circumventing the state space explosion problem. In doing this, we propose a methodology for analyzing QPN models by means of discrete event simulation. The methodology shows how to simulate QPN models and analyze the output data from simulation runs. We validate our approach by applying it to study several different QPN models, ranging from simple models to models of realistic systems. The performance of point and interval estimators implemented in SimQPN is subjected to a rigorous experimental analysis.     

基于Petri网结构分析的监控器综合

在基于Petri网建模的离散事件系统中, 提出利用局部关联信息进行约束转换, 并实现Petri网结构监控器综合的方法. 对以Parikh矢量约束形式给出的控制规范, 不可控不可观变迁会导致约束成为非法约束, 分析了不可控变迁的前向关联结构和不可观变迁的后向关联结构, 利用局部关联变迁实现对不可控和不可观变迁的间接控制, 从而将非法矢量约束转换为合法约束, 并保证初始控制规范的实现. 与基于矩阵的监控器综合方法相比, 本文的方法只需利用局部信息, 最后通过实例对该方法进行了说明.     

离散事件控制器综合与重构的研究

讨论了离散事件控制器快速综合与重构方面研究的意义以及存在的问题,介绍了基于改进的网重写系统的Petri网离散事件控制器快速综合与重构理论与方法的研究进展及其仿真系统开发。     

Supervisor Synthesis for Real-Time Discrete Event Systems

This paper introduces a formal framework to logically analyze and control real-time discrete event systems (RTDESs). Time Petri nets are extended to controlled time Petri nets (CtlTPNs) to model the dynamics of RTDESs that can be controlled by real-time supervisors. The logical behaviors of CtlTPNs are represented by control class graphs (CCGs) which are untimed automata with timing and control information in their state transition labels. We prove that the CCG corresponding to a CtlTPN expresses completely the logical behavior of the CtlTPN. The real-time supervisor is based on a nondeterministic logical supervisor for the CCG, including the delay for control computations to ensure the supervisor is acceptable in a true real-time environment. We prove the existence of a unique maximal controllable sublanguage of a given specification language and present an algorithm to construct the sublanguage. We also prove that the real-time supervisor meets the prespecified real-time behavior and present an online control algorithm to implement real-time supervisors. The concepts and algorithms are illustrated for an example of packet reception processes in a communication network.     

A control synthesis approach for time discrete event systems

In this paper, we introduce a control synthesis method for discrete event systems whose behavior is dependent on explicit values of time. Our goal is to control the occurrence dates of the controllable events so that the functioning of the system respects given specifications. The system to be controlled is modeled by a time Petri net. In a previous work we proposed a systematic method to build the timed automaton which models the exact behavior of a time Petri net. Furthermore, the forbidden behaviors of the system are modeled by forbidden timed automaton locations. This paper focuses on the control synthesis method, which consists in computing new firing conditions for the timed automaton transitions so that the forbidden locations are no longer reachable.     

Integration of Petri nets and moment generating function approaches for system performance evaluation

This article integrates arbitrary stochastic Petri nets (ASPN) and moment generating function approaches for performance evaluation of discrete event dynamic systems (DEDS). These systems include computer-integrated manufacturing systems, resource-shared distributed systems, and communication networks. ASPN can describe various DEDS in which the time duration for activities may be a random variable of arbitrary distributions. In ASPN models, transitions with firing delays of general distributions are used to model these activities. Using our proposed performance analysis methodology, we first represent a system as an ASPN model, then generate its reachability graph and convert it into a state machine Petri net, derive the transfer functions of interesting performance measures through stepwise reductions, and finally obtain the analysis results. This method makes it possible to obtain analytical solutions of important performance indices. We use a robotic assembly system to illustrate the method. We obtain several important performance measures of a closed-form. Finally, we discuss the limitations of this approach and future research.     

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     

基于Petri网的分布式系统并发进程的死锁检测

分布式系统中的并发进程具有明显的并发、异步及分布性,而Petri网是模拟与分析并发、异步、分布式系统的有效工具.为此通过引入Petri网,给出了分布式系统局部并发进程等待的Petri网模型及死锁检测方法,提出了全链路合成的概念,利用全链路合成技术组装了全局并发进程等待的Petri网模型,给出了判断整个系统是否出现死锁的充分必要条件.     

Shrinking of Time Petri nets

The problem of the synthesis of time bounds enforcing good properties for reactive systems has been much studied in the literature. These works mainly rely on dioid algebra theory and require important restrictions on the structure of the model (notably by restricting to timed event graphs). In this paper, we address the problems of existence and synthesis of shrinkings of the bounds of the time intervals of a time Petri net, such that a given property is verified. We show that this problem is decidable for CTL properties on bounded time Petri nets. We then propose a symbolic algorithm based on the state class graph for a fragment of CTL. If the desired property “includes” k-boundedness, the proposed algorithm terminates even if the net is unbounded. A prototype has been implemented in our tool Romeo and the method is illustrated on a small case study from the literature.