Decentralised control of continuous Petri nets

This paper focuses on decentralised control of systems modelled by continuous Petri nets, in which a target marking control problem is discussed. In some previous works, an efficient ON/OFF strategy-based minimum-time controller was developed. Nevertheless, the convergence is only proved for subclasses like Choice-Free nets. For a general net, the pre-conditions of applying the ON/OFF strategy are not given; therefore, the application scope of the method is unclear. In this work, we provide two sufficient conditions of applying the ON/OFF strategy-based controller to general nets. Furthermore, an extended algorithm for general nets is proposed, in which control laws are computed based on some limited information, without knowing the detailed structure of subsystems.     

一类受控Petri网的控制器设计

通过挖掘Petri网的内在的结构特性, 获得了一种新的解决禁止状态避免问题的控制器设计方法. 这种设计方法适用于一类具有特殊结构的受控Petri网 (即所有前向路径子网是状态机 )的状态反馈控制器设计. 在非并发的假设条件下, 所综合的控制器是最大允许.     

Colored timed Petri nets for modeling and analysis of cluser tools

In this paper, a colored timed resource‐oriented Petri net (CTROPN) is developed to model the cluster tools in semiconductor fabrication. It is structurally simple and concise, since each module in a cluster tool corresponds to a unique place in CTROPN. It is also powerful in modeling the qualitative and temporal behavior of the cluster tools with a single‐blade or dual‐blade robot. The initial transient behavior, steady‐state behavior and the final transient behavior can all be investigated through a single model. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Feasibility of piecewise-constant control sequences for timed continuous Petri nets

In this study, the determination of control actions for timed continuous Petri nets is investigated by the characterisation of attractive regions in marking space. In particular, attraction in finite time, which is important for practical issues, is considered. Based on the characterisation of attractive regions, the domain of admissible piecewise constant control actions is computed, and sufficient conditions to verify the feasibility of the control objectives are proposed. As a consequence, an iterative procedure is presented to compute piecewise constant control actions that correspond to local minimum time control for timed continuous Petri nets.     

Performance analysis using Petri nets

The purpose of this paper is to focus on the implementation issues associated with using Petri nets for the performance analysis of discrete event dynamic systems while demonstrating several applications in manufacturing systems. Practical modeling issues will be discussed and several applications will be presented that illustrate the advantages and limitations of this methodology. These issues lead to the definition of several research problems in Petri nets for performance analysis.     

Event‐driven model predictive control of timed hybrid Petri nets

Hybrid Petri nets represent a powerful modeling formalism that offers the possibility of integrating, in a natural way, continuous and discrete dynamics in a single net model. Usual control approaches for hybrid nets can be divided into discrete‐time and continuous‐time approaches. Continuous‐time approaches are usually more precise, but can be computationally prohibitive. Discrete‐time approaches are less complex, but can entail mode‐mismatch errors due to fixed time discretization. This work proposes an optimization‐based event‐driven control approach that applies on continuous time models and where the control actions change when discrete events occur. Such an approach is computationally feasible for systems of interest in practice and avoids mode‐mismatch errors. In order to handle modelling errors and exogenous disturbances, the proposed approach is implemented in a closed‐loop strategy based on event‐driven model predictive control. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimal stationary behavior for a class of timed continuous Petri nets

In this paper, we consider a deterministic timed continuous Petri net model where conflicts at places are solved by using stationary routing parameters. We show how to compute the stationary firing rate for all transitions via linear programming, so as to determine the optimal routing parameters that maximize user-defined linear functions of the firing rates. Finally, we discuss the relations with discrete Petri nets.     

Deciding the liveness for a subclass of weighted Petri nets based on structurally circular wait

Weighted Petri nets as a kind of formal language are widely used to model and verify discrete event systems related to resource allocation like flexible manufacturing systems. System of Simple Sequential Processes with Multi-Resources (S³PMR, a subclass of weighted Petri nets and an important extension to the well-known System of Simple Sequential Processes with Resources, can model many discrete event systems in which (1) multiple processes may run in parallel and (2) each execution step of each process may use multiple units from multiple resource types. This paper gives a necessary and sufficient condition for the liveness of S³PMR. A new structural concept called Structurally Circular Wait (SCW) is proposed for S³PMR. Blocking Marking (BM) associated with an SCW is defined. It is proven that a marked S³PMR is live if and only if each SCW has no BM. We use an example of multi-processor system-on-chip to show that SCW and BM can precisely characterise the (partial) deadlocks for S³PMR. Simultaneously, two examples are used to show the advantages of SCW in preventing deadlocks of S³PMR. These results are significant for the further research on dealing with the deadlock problem.     

基于有限容量库所的离散事件系统的Petri网控制器综合——第2部分

FCP方法的基本思想已在第一部分作了介绍. 第二部分给出了离散事件系统在最一般情况下约束的Petri网控制器的设计方法, 并证明FCP方法是最大容许控制的. 此外, 已有文献里的自动导航车辆协调系统的例子将被用来说明FCP方法所具有的优点和特点.     

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.     

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.     

Discrete event diagnosis using labeled Petri nets. An application to manufacturing systems

In this paper an approach to on-line diagnosis of discrete event systems based on labeled Petri nets is presented. The approach is based on the notion of basis markings and justifications and it can be applied both to bounded and unbounded Petri nets whose unobservable subnet is acyclic. Moreover it is shown that, in the case of bounded Petri nets, the most burdensome part of the procedure may be moved off-line, computing a particular graph called Basis Reachability Graph.Finally, the effectiveness of the proposed procedure is analyzed applying a MATLAB diagnosis toolbox we developed to a manufacturing example taken from the literature.     

The fundamental closed-form solution of control-related states of kth order S3PR system with left-side non-sharing resource places of Petri nets

Due to the state explosion problem, it has been unimaginable to enumerate reachable states for Petri nets. Chao broke the barrier earlier by developing the very first closed-form solution of the number of reachable and other states for marked graphs and the kth order system. Instead of using first-met bad marking, we propose ‘the moment to launch resource allocation’ (MLR) as a partial deadlock avoidance policy for a large, real-time dynamic resource allocation system. Presently, we can use the future deadlock ratio of the current state as the indicator of MLR due to which the ratio can be obtained real-time by a closed-form formula. This paper progresses the application of an MLR concept one step further on Gen-Left kth order systems (one non-sharing resource place in any position of the left-side process), which is also the most fundamental asymmetric net structure, by the construction of the system's closed-form solution of the control-related states (reachable, forbidden, live and deadlock states) with a formula depending on the parameters of k and the location of the non-sharing resource. Here, we kick off a new era of real-time, dynamic resource allocation decisions by constructing a generalisation formula of kth order systems (Gen-Left) with r^* on the left side but at arbitrary locations.     

Suboptimal liveness-enforcing supervisor design for a class of generalised Petri nets using partial siphon enumeration and mathematical programming

This article develops a deadlock prevention policy for a class of generalised Petri nets, which can well model a large class of flexible manufacturing systems. The analysis of such a system leads us to characterise the deadlock situations in terms of the insufficiently marked siphons in its generalised Petri-net model. The proposed policy is carried out in an iterative way. At each step a minimal siphon is derived from a maximal deadly marked siphon that is found by solving a mixed integer programming (MIP) problem. An algorithm is formalised that can efficiently compute such a minimal siphon from a maximal one. A monitor is added for a derived minimal siphon such that it is max-controlled if it is elementary with respect to the siphons that have been derived. The liveness of the controlled system is decided by the fact that no siphon can be derived due to the MIP solution. After a liveness-enforcing net supervisor computed without complete siphon enumeration, the output-arcs of the additional monitors are rearranged such that the monitors act while restricting the system less. Examples are presented to demonstrate the proposed method.     

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．     

Real time identification of discrete event systems using Petri nets

The paper defines the identification problem for Discrete Event Systems (DES) as the problem of inferring a Petri Net () model using the observation of the events and the available output vectors, that correspond to the markings of the measurable places. Two cases are studied considering different levels of the system knowledge. In the first case the place and transition sets are assumed known. Hence, an integer linear programming problem is defined in order to determine a modelling the DES. In the second case the transition and place sets are assumed unknown and only an upper bound of the number of places is given. Hence, the identification problem is solved by an identification algorithm that observes in real time the occurred events and the corresponding output vectors. The integer linear programming problem is defined at each observation so that the can be recursively identified. Some results and examples characterize the identified systems and show the flexibility and simplicity of the proposed technique. Moreover, an application to the synthesis of supervisory control of systems via monitor places is proposed.     

Fault detection for discrete event systems using Petri nets with unobservable transitions

In this paper we present a fault detection approach for discrete event systems using Petri nets. We assume that some of the transitions of the net are unobservable, including all those transitions that model faulty behaviors. Our diagnosis approach is based on the notions of basis marking and justification, that allow us to characterize the set of markings that are consistent with the actual observation, and the set of unobservable transitions whose firing enable it. This approach applies to all net systems whose unobservable subnet is acyclic. If the net system is also bounded the proposed approach may be significantly simplified by moving the most burdensome part of the procedure off-line, thanks to the construction of a graph, called the basis reachability graph.     

混成时空Petri网的CPS实时事件模型

在分析网络物理系统（ CPS）特点的基础上,提出了一种新的CPS体系结构,并对事件进行形式化定义。提出了一种新的CPS物理实体的形式化建模方法。在Petri网的基础上引入时空因素和连续变量,构造了混成时空Petri网（ HSPN）模型,使其不仅能够描述物理实体逻辑和时间层次的行为,而且能够描述物理实体位置变迁所引起的状态变化。将其应用于实时事件CPS模型设计,以医疗控制系统为例,分析建模方法的可行性。     

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.