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

Zhao, Mi; Li, Zhiwu; Hu, Hesuan

doi:10.1080/00207720903171779

Cited by 25 publications

(16 citation statements)

References 24 publications

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“…Petri nets are a formal method to model and analyse discrete event systems (Brooks, Zhu, Lamb, & Iyengar, 2004;Hruz & Zhou, 2007;Li & Zhou, 2009;van der Aalst et al, 2011;Wu & Zhou, 2010;Xiao & Lee, 2008;Zhao, Li, & Hu, 2010;Zhou & Fanti, 2005;Zhou & Venkatesh, 1998). They can well characterise the system features such as concurrency, choice, and synchronous/asynchronous communication.…”

Section: Introductionmentioning

confidence: 97%

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

Liu

Chen

2014

International Journal of Systems Science

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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 (S 3 PMR, 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 S 3 PMR. A new structural concept called Structurally Circular Wait (SCW) is proposed for S 3 PMR. Blocking Marking (BM) associated with an SCW is defined. It is proven that a marked S 3 PMR 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 S 3 PMR. Simultaneously, two examples are used to show the advantages of SCW in preventing deadlocks of S 3 PMR. These results are significant for the further research on dealing with the deadlock problem.

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Section: Introductionmentioning

confidence: 97%

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

Liu

Chen

2014

International Journal of Systems Science

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“…Compared with the policy by Huang et al, 250 it is shown that fewer monitors are needed. Later, Zhao et al 246 further extend the iterative method to a more general class, called S 4 PR nets. In order to achieve a better method that can precisely and immediately decide the controllability of dependent SMSs via their elementary siphons' control without using the time-consuming MIP tests, the work by Liu et al 288 proposes a more precise sufficient condition for the controllability of dependent SMSs and proves that it is better than the condition in the work by Li and Zhou.…”

Section: Elementary Siphon-based Approachesmentioning

confidence: 99%

“…Based on the elementary siphons, a variety of deadlock control policies 216,[229][230][231][243][244][245][246] are developed for synthesizing liveness-enforcement supervisors. However, in generalized Petri nets, multiple resource requirements should be considered sufficiently in identifying a set of elementary siphons.…”

Section: Augmented Elementary Siphons In Generalized Petri Netsmentioning

confidence: 99%

Deadlock analysis and control based on Petri nets: A siphon approach review

Hou

Barkaoui

2017

Advances in Mechanical Engineering

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Deadlocks should be eliminated in highly automated manufacturing systems since their occurrence implies the stoppage of the whole or partial system operation. Over the past decades, Petri nets are increasingly becoming one of the most popular and full-fledged mathematical tools to deal with deadlock problems due to their inherent characteristics. In a Petri net formalism, liveness is an important property of system safeness, which implies the absence of global and local deadlock situations in an automated manufacturing system. The liveness assessment can be performed by verifying the satisfiability of certain predicates on siphons, a well-known structural object in Petri nets. Therefore, siphons have received much attention to analyze and control systems modeled with Petri nets. Particularly, elementary siphon theory plays a key role in the development of structurally simple liveness-enforcing Petri net supervisors, leading to a variety of deadlock control approaches. This survey studies on the state-of-the-art elementary siphon theory of Petri nets including refined concepts of elementary siphons and their extended version, computation methods of siphons and elementary ones, controllability conditions, and their application to deadlock control. As a reference, this work attempts to provide a comprehensive and updated research survey on siphons, elementary siphons, and their applications to the deadlock resolution in Petri nets.

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“…However, the siphon-based control policies for G-systems are of exponential complexity due to a complete or partial siphon enumeration. 50,51 Furthermore, the behavioral permissiveness problem is referred to as the fact that permissive behavior is overly restricted by the siphon-based control policies, that is to say, the supervisor excludes some safe (admissible) states. This is so since the output arcs of a monitor are led to the source transitions of the net model, which limits the number of workpieces being released into and processed by the system.…”

Section: Motivation Of Deadlock Prevention Policy For G-systemsmentioning

confidence: 99%

“…However, the computation of RG in a very complex net system cannot be carried out using the global-conquer methods as in Zhao and colleagues. 51,54 In order to improve the computational efficiency of the supervisor, this section develops a D-C-based deadlock control algorithm for G-systems. At first, the definition of non-blockingness in a G-system is depicted as follows:…”

Section: Motivation Of Deadlock Prevention Policy For G-systemsmentioning

confidence: 99%

Near-optimal supervisory control of flexible manufacturing systems using divide-and-conquer iterative method

Zhao

Uzam

Hou

2016

Advances in Mechanical Engineering

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This article proposes an iterative deadlock resolution method for flexible manufacturing systems modeled with G-systems. To design a non-blocking controlled system with maximally permissive behavior in a G-system (GS), a reachability graph-based analysis technology is utilized. Since the reachability graph of a large-scale GS easily becomes unmanageable, an optimal non-blocking supervisor becomes a challenging problem in a GS. To facilitate this problem, the Divide-andConquer approach is a good choice for complex G-systems. First, an uncontrolled GS resolves into a number of associated subnets. Then, every subnet suffering from deadlocks is utilized to design the liveness-enforcing supervisor for the original GS. Thus, additional monitors can be obtained if the liveness of all subnets is achieved. Subsequently, a partially controlled GS is derived by including all monitors within the GS, and its liveness can be ensured by designing a new set of monitors. Consequently, a non-blocking GS is derived. The major advantage of the proposed method is that a nonblocking supervisor with near-optimal behavioral permissiveness can be obtained in general. Finally, a typical GS example popularly studied in the literature is applied to demonstrate the validity and the availability of the method in this article.

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

Cited by 25 publications

References 24 publications

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

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

Deadlock analysis and control based on Petri nets: A siphon approach review

Near-optimal supervisory control of flexible manufacturing systems using divide-and-conquer iterative method

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