Analysis of Hybrid Systems Based on Hybrid Net Condition/Event System Model

In thispaper, hybrid net condition /event systems are introducedas a model for hybrid systems. The model consists of a discretetimed Petri net and a continuous Petri net which interact eachother through condition and event signals. By introducing timeddiscrete places in the model, timing constraints in hybrid systemscan be easily described. For a class of hybrid systems that canbe described as linear hybrid net condition /eventsystems whose continuous part is a constant continuous Petrinet, two methods are developed for their state reachability analysis.One is the predicate-transformation method, which is an extensionof a state reachability analysis method for linear hybrid automata.The other is the path-based method, which enumerates all possiblefiring seqenences of discrete transitions and verifies if a givenset of states can be reached from another set by firing a sequenceof discrete transitions. The verification is performed by solvinga constraint satisfaction problem. A technique that adds additionalconstraints to the problem when a discrete state is revisitedalong the sequence is developed and used to prevent the methodfrom infinite enumeration. These methods provide a basis foralgorithmic analysis of this class of hybrid systems.     

On Hybrid Petri Nets

Petrinets (PNs) are widely used to model discrete event dynamic systems(computer systems, manufacturing systems, communication systems,etc). Continuous Petri nets (in which the markings are real numbersand the transition firings are continuous) were defined morerecently; such a PN may model a continuous system or approximatea discrete system. A hybrid Petri net can be obtained if onepart is discrete and another part is continuous. This paper isbasically a survey of the work of the authors' team on hybridPNs (definition, properties, modeling). In addition, it containsnew material such as the definition of extended hybrid PNs andseveral applications, explanations and comments about the timingsin Petri nets, more on the conflict resolution in hybrid PNs,and connection between hybrid PNs and hybrid automata. The paperis illustrated by many examples.     

Timing and liveness in continuous Petri nets

Fluidification constitutes a relaxation technique for studying discrete event systems through fluidified approximated models, thus avoiding the state explosion problem. Moreover, the class of continuous models thus obtained may be interesting in itself. In Petri nets, fluidification leads to the so-called continuous Petri nets, which are technically hybrid models. Under infinite server semantics, timing a continuous Petri net model preserves the liveness property, but the converse is not necessarily true, and if the autonomous net model is not live, the timing may transform it into a live model. In this paper, we investigate the conditions on the firing rates of timed continuous models that make a given continuous system live.     

基于资源配置混杂Petri网的混杂系统生产过程建模

为了增强混杂Ｐｅｔｒｉ网解决资源共享和资源冲突的能力,定义一种新的混杂Ｐｅｔｒｉ网模型———资源配置混杂Ｐｅｔｒｉ网,提出了相应的使能和激发规则．将对连续变迁和离散变迁的控制作用引入混杂Ｐｅｔｒｉ网,同时,增加了资源配置变迁和资源释放变迁,用于有效分配可重复利用的资源．以典型的混杂生产过程为例,研究混杂系统生产过程建模．研究结果表明,所定义的模型描述能力强,模型语义正确合理,能够有效描述和分析混杂系统生产过程．     

Timed Petri Nets in Hybrid Systems: Stability and Supervisory Control

In this paper, timed Petri nets are used to model and control hybrid systems. Petri nets are used instead of finite automata primarily because of the advantages they offer in dealing with concurrency and complexity issues. A brief overview of existing results on hybrid systems that are based on Petri nets is first presented. A class of timed Petri nets named programmable timed Petri nets (PTPN) is then used to model hybrid systems. Using the PTPN, the stability and supervisory control of hybrid systems are addressed and efficient algorithms are introduced. In particular, we present sufficient conditions for the uniform ultimate boundness of hybrid systems composed of multiple linear time invariant plants which are switched between using a logical rule described by a Petri net. This paper also examines the supervisory control of a hybrid system in which the continuous state is transfered to a region of the state space in a way that respects safety specifications on the plant's discrete and continuous dynamics.     

神光III控制系统的故障建模与分析

应用混合随机Petri网对神光III控制系统的故障进行了建模,并应用Visobj Net对建立的故障模型进行了仿真分析。网络化控制系统是一个离散和连续相结合的混合动态系统,具有动态、并发及同步等特征;神光III控制系统就是网络化控制技术在武器装备上的一个典型应用;对于复杂系统的建模和分析,Petri网是一个非常有效的工具。Petri网已经被证明是离散事件或异步系统很好的建模和分析工具,混合随机Petri网是Petri网的一个扩展,具有强大的建模功能。仿真结果表明,所建立的模型是正确的。     

Discrete event representation of qualitative models using Petrinets

The paper discusses how Petri nets may be used for the qualitative modeling of physical systems. The qualitative state of a system is represented by the marking of the net. The crossing of a landmark value corresponds to the firing of a transition. We give a formal procedure to construct a Petri net model corresponding to a given set of qualitative equations. The approach can be used to study both autonomous systems and systems with forcing inputs. The dynamic behavior of the system can be studied as sequences of reachable markings of the net and can be computed with standard Petri net execution techniques. This approach also leads to a simple framework for the study of hybrid systems, i.e., systems whose behavior is described by both continuous and discrete event dynamics. Several examples, with applications to diagnosis and control, are fully discussed.     

Steady-state performance evaluation of continuous mono-T-semiflow Petri nets

The number of states in discrete event systems can increase exponentially with respect to the size of the system. A way to face this state explosion problem consists of relaxing the system model, for example by converting it to a continuous one. In the scope of Petri nets, the firing of a transition in a continuous Petri net system is done in a real amount. Hence, the marking (state) of the net system becomes a vector of non-negative real numbers. The main contribution of the paper lies in the computation of throughput bounds for continuous Petri net systems with a single T-semiflow. For that purpose, a branch and bound algorithm is designed. Moreover, it can be relaxed and converted into a linear programming problem. Some conditions, under which the system always reaches the computed bounds, are extracted. The results related to the computation of the bounds can be directly applied to a larger class of nets called mono T-semiflow reducible.     

爬行机器人的分层可控混成Petri网建模研究

飞机表面爬行机器人是一个复杂的离散事件和连续动态事件相结合的混成运动系统,为描述系统的静态特性和动态行为,提出一种分层可控混成Petri网模型.依据爬行运动机构定义了Petri网模型组成元素,建立了爬行机器人单轴和双轴分层可控混成Petri网,该模型可接收上层运动轨迹指令并输出爬行动作序列.实验表明,基于该模型实施的飞...     

Generalised Batches Petri Net: Hybrid Model For High Speed Systems With Variable Delays

Recently, the possibilityof associating both discrete events and continuous time behaviourin the same formalism has generated a considerable interest inthe Petri net paradigm. A central issue in this field is theconcept of Hybrid Petri net which consists in continuous transitionsand places holding non negative real number, and discrete transitionsand places holding integer tokens. By adding a new type of nodes,batch transitions and batch places, Batches Petri nets have beendefined. A batch node combines both a discrete event and a linearcontinuous dynamic behaviour in a single structure. Batches Petrinets can then be used in the control design and performance analysisof high-speed systems composed of continuous transfer elementswhich introduce variable delays on continuous flows. In thispaper, the complete formalism of Generalised Batches Petri netsis given through the definition of the model, the enabling andfiring rules, the time analysis methods, and two examples illustratethese notions.     

面向原油库存管理过程的Petri网建模

石油化工工业属于典型的连续型生产工业,但在连续生产过程中又包含有离散变量, 具有明显的混杂动态系统特征.对于这样的混杂动态系统,混合Petri网是一种有效的建模方法.文章在已有的混合Petri网结构基础上,在离散变迁激发规则中加入了逻辑控制条件,并对原油库存管理过程这一兼有连续时间特性和离散事件特性的混合动态系统进行建模,并通过建模实例验证了其有效性和灵活性,从而为解决原油库存问题提供了具有参考价值的方法.     

Basic Server Semantics and Performance Monotonicity of Continuous Petri Nets

Continuous Petri nets were introduced as an approximation to deal with the state explosion problem which can appear in discrete event models. When time is introduced, the flow through a fluidified transition can be defined in many ways. The most used in literature are constant and variable speed (David and Alla, Discrete, continuous and hybrid Petri nets, Springer-Verlag, 2005), which can be seen as some kind of finite and infinite server interpretations of the transitions behavior, and derived from stochastic (discrete) Petri nets (Silva and Recalde, Annu Rev Control 28(2):253–266, 2004). In this paper we will compare the results obtained with both relaxations for the broad class of mono-T-semiflow reducible nets, and prove that, under some frequently true conditions, infinite server semantics offers a throughput which is closer to the throughput of the discrete system in steady state. In the second part, it will be proved that the throughput of mono-T-semiflow reducible net systems is monotone with respect to the speed of the transitions and the initial marking of the net.     

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.     

基于Time Petri Nets的实时系统资源冲突检测

Time Petri Nets在实时系统的建模和性能分析中得到广泛应用,而冲突是Petri网及其扩展模型的重要行为,解决冲突是正确分析模型动态行为的关键.目前随机Petri网、混合Petri网和区间速率连续Petri网的冲突检测方法由于没有考虑到时间约束因此无法在TPN网中使用.时间约束的引入使得Time Petri Nets模型的使能和触发语义比Petri网模型的语义复杂,冲突检测变得更加困难.为了计算冲突发生的时间和概率,首先根据时间约束,给出了变迁持续使能时延迟区间的计算方法,并证明了该方法的合理性和完备性;然后在此基础上定义并证明了Time Petri Nets模型中不冲突的检测方法;并提出了Time Petri Nets模型的冲突检测方法,给出了冲突时间区间和变迁实施概率的计算方法;最后通过实例验证说明了该方法的正确性和有效性.     

Hybrid Petri net based modeling for biological pathway simulation

Hybrid Petri net (HPN) is an extension of the Petri net formalism, which enables us to handle continuous information in addition to discrete information. Firstly, this paper demonstrates how biological pathways can be modeled by the integration of discrete and continuous elements, with an example of the λ phage genetic switch system including induction and retroregulation mechanisms. Although HPN allows intuitive modeling of biological pathways, some fundamental biological processes such as complex formation cannot be represented with HPN. Thus, this paper next provides the formal definition of hybrid functional Petri net with extension (HFPNe), which has high potential for modeling various kinds of biological processes. Cell Illustrator is a software tool developed on the basis of the definition of HFPNe. Hypothesis creation by Cell Illustrator is demonstrated with the example of the cyanobacterial circadian gene clock system. Finally, our ongoing tasks, which include the development of a computational platform for systems biology, are presented.     

基于混合随机Petri网的一类混合系统的模型及稳定性

混合动态系统是包含离散事件系统（ＤＥＳ）和连续变量系统（ＣＶＳ）的复杂系统。讨论了一类每个离散状态包含一个连续动态系统,且离散事件具有Ｍａｒｋｏｖ链性质的随机混合系统,在提出利用混合随机Ｐｅｔｒｉ网的建模方法的基础上,给出混合均方稳定的概念、稳定性和可镇定条件,最后以一个简单的例子做子说明和仿真。     

A modeling strategy for hybrid systems based on event structures

This paper considers hybrid systems which are continuous/discrete-time systems interacting with a decision maker which oversees the control and structure of the continuous/discrete-time system. These two segments combine with a processor which evaluates data to produce a three-segment model of a hybrid system having sufficient flexibility to represent a broad range of real-time situations and sufficient generality to incorporate the essential aspects of other models into a single framework. In particular the paper uses a graphically expressive controlled Petri net formulation of the decision maker and any of the usual models for the continuous/discrete-time system. Interaction between the systems occurs via three types of events: continuous/discrete-time events, decision-making events, and processor events. These types of events and their composition are rigorously defined to produce event structures and event histories. These events and event histories are used for the domain of interaction functions which specify the channels of communication between the three essential segments of the hybrid system. The event-based domains allow the disassociation of these communication channels from dependence on particular kinds of models or applications. The range of the interaction functions are binary vector-valued indicating the activation/deactivation processes in the respective segments. The entire modeling strategy is motivated by applications and models found in the literature especially flexible manufacturing systems and the C-net model of a hybrid system.This work was partially supported by the National Science Foundation under Grant No. ECS-8800910.     

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.     

基于扩展混成Petri网的CPS无人车系统建模与分析

信息物理融合系统(Cyber-Physical System,CPS)是一个集计算系统、通信系统、感知系统、控制系统和物理系统于一体的复杂系统,其行为是一种由离散计算过程与连续物理过程深度融合并紧密交互的混成行为。针对这种特性,采用混成Petri网对CPS建模,并在此基础上添加时间约束,即对离散变迁关联一个延迟时间,对连续变迁关联一个激发速率函数,同时引入抑止弧和测试弧的概念以提高Petri网的表达能力,由此提出一种新的模型——扩展混成Petri网模型。然后,对CPS应用中无人驾驶车辆系统的躲避障碍物场景进行建模,将建立的模型按照一定的规则转化为与之对应的Simulink模型,并通过Matlab仿真对系统行为及属性进行分析。