New controllability condition for siphons in a class of generalised Petri nets

Liu, Gaiyun; Li, Z.; Zhong, Cheng

doi:10.1049/iet-cta.2009.0264

Cited by 31 publications

(51 citation statements)

References 42 publications

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“…In this section, we first briefly review the concepts of the max-, max -, and max -controllability conditions of a siphon in a GS 3 PR net in Barkaoui and Pradat-Peyre (1996), Chao (2007), Zhong and Li (2010), and Liu et al (2010a) by an example, which motivates this study.…”

Section: Motivationmentioning

confidence: 99%

“…In our previous work (Liu et al 2010a), we presented a new concept called max -controllability condition of siphons to relax the max -controllability condition.…”

Section: Max -Controlled Siphonsmentioning

confidence: 99%

“…Definition 13 (Liu et al 2010a): Let S be a siphon in a wellmarked S 4 R (N, M 0 ). S is said to be max -marked at M ∈ R(N, M 0 ) if at least one of the following conditions holds:…”

Section: Max -Controlled Siphonsmentioning

confidence: 99%

“…A Petri net is ordinary if the weight of each arc is one while it is generalised if there exists an arc whose weight is greater than or equal to two. Systems of simple sequential processes with resources (S 3 PR) (Ezpeleta et al 1995) and systems of sequential systems with shared resources (S 4 R) (S 4 R in Liu, Li, and Zhong 2010a are equivalent to S 4 PR in Tricas, García-Vallés, Colom, and Ezpeleta 2000, and S 3 PGR 2 in Park and Reveliotis 2001) are typical classes of ordinary Petri nets and generalised Petri nets, respectively. Both S 3 PR and S 4 R are composed of a set of state machines and a set of resource places.…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by this notorious issue, researchers propose a number of concepts involving the controllability of siphons in a generalised Petri net, such as max-controllability (Barkaoui and Pradat-Peyre 1996), max -controllability (Chao 2007;Zhong and Li 2010), and max -controllability (Liu et al 2010a). The proposal of these concepts aims to reduce the conservativeness 2 of a International Journal of Systems Science 1149 deadlock prevention policy whose development is based on the siphon control.…”

Section: Introductionmentioning

confidence: 99%

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Necessary and sufficient liveness condition of GS³PR Petri nets

Liu

Barkaoui

2013

International Journal of Systems Science

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Structural analysis is one of the most important and efficient methods to investigate the behaviour of Petri nets. Liveness is a significant behavioural property of Petri nets. Siphons, as structural objects of a Petri net, are closely related to its liveness. Many deadlock control policies for flexible manufacturing systems (FMS) modelled by Petri nets are implemented via siphon control. Most of the existing methods design liveness-enforcing supervisors by adding control places for siphons based on their controllability conditions. To compute a liveness-enforcing supervisor with as much as permissive behaviour, it is both theoretically and practically significant to find an exact controllability condition for siphons. However, the existing conditions, max, max , and max -controllability of siphons are all overly restrictive and generally sufficient only. This paper develops a new condition called max * -controllability of the siphons in generalised systems of simple sequential processes with resources (GS 3 PR), which are a net subclass that can model many real-world automated manufacturing systems. We show that a GS 3 PR is live if all its strict minimal siphons (SMS) are max * -controlled. Compared with the existing conditions, i.e., max-, max -, and max -controllability of siphons, max * -controllability of the SMS is not only sufficient but also necessary. An example is used to illustrate the proposed method.

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Section: Motivationmentioning

confidence: 99%

“…In our previous work (Liu et al 2010a), we presented a new concept called max -controllability condition of siphons to relax the max -controllability condition.…”

Section: Max -Controlled Siphonsmentioning

confidence: 99%

“…Definition 13 (Liu et al 2010a): Let S be a siphon in a wellmarked S 4 R (N, M 0 ). S is said to be max -marked at M ∈ R(N, M 0 ) if at least one of the following conditions holds:…”

Section: Max -Controlled Siphonsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Necessary and sufficient liveness condition of GS³PR Petri nets

Liu

Barkaoui

2013

International Journal of Systems Science

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A deadlock prevention approach for flexible manufacturing systems with uncontrollable transitions in their Petri net models

Zhu

2011

Asian Journal of Control

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Deadlocks are a highly undesired situation in a fully automated flexible manufacturing system, whose occurrences are tied to the existence of shared resources that are competed by different production processes. In the last two decades, a fair amount of research has been done on deadlock analysis and control for flexible manufacturing systems, leading to a variety of strategies in the literature. Petri nets are a promising mathematical tool to handle deadlock problems in flexible manufacturing systems. However, most deadlock control policies based on a Petri net formalism assume that all the transitions in a plant model are controllable. However, uncontrollability of events are a natural feature in a real-world production system. This paper proposes a deadlock prevention policy for a class of Petri nets by considering the existence of uncontrollable transitions. Deadlocks are prevented by adding monitors to a plant Petri net model, whose addition does not inhibit the firings of uncontrollable transitions. Linear programming techniques are employed to find transitions to which a monitor points in order that a more permissive liveness-enforcing Petri net supervisor can be found. A number of manufacturing examples are used to demonstrate the proposed methods.

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New Controllability Condition for Siphons in Ws³PR Nets

Guan

Wang

2014

Asian Journal of Control

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Existing policies for deadlock control are mainly based on siphons due to their ability to indicate deadlocks, and can be used as a powerful tool to deal with deadlock situations in flexible manufacturing systems. In order to avoid deadlocks, researchers often add monitors to control siphons. This may result in redundant monitors, unnecessary cost, and restriction of the behavior permissiveness. For example, for a system of sequential systems with shared resources (S4R), the existing deadlock control policies based on max, max′ or max′′‐controlled siphons tend to overly restrict the behavior of a controlled system. To ensure maximal permissive behavior of controlled systems, a new concept of siphon controllability named W‐control is defined and then a sufficient and necessary condition under which a WS3PR is live if all its siphons are W‐controlled. Examples are given to demonstrate them.

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New controllability condition for siphons in a class of generalised Petri nets

Cited by 31 publications

References 42 publications

Necessary and sufficient liveness condition of GS³PR Petri nets

Necessary and sufficient liveness condition of GS³PR Petri nets

A deadlock prevention approach for flexible manufacturing systems with uncontrollable transitions in their Petri net models

New Controllability Condition for Siphons in Ws³PR Nets

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New controllability condition for siphons in a class of generalised Petri nets

Cited by 31 publications

References 42 publications

Necessary and sufficient liveness condition of GS3PR Petri nets

Necessary and sufficient liveness condition of GS3PR Petri nets

A deadlock prevention approach for flexible manufacturing systems with uncontrollable transitions in their Petri net models

New Controllability Condition for Siphons in Ws3PR Nets

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Necessary and sufficient liveness condition of GS³PR Petri nets

Necessary and sufficient liveness condition of GS³PR Petri nets

New Controllability Condition for Siphons in Ws³PR Nets