Incremental approach to computation of elementary siphons for arbitrary simple sequential processes with resources

Chao, Daniel Yuh

doi:10.1049/iet-cta:20070130

Cited by 30 publications

(23 citation statements)

References 6 publications

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“…In [16], a polynomial time algorithm was proposed to find elementary siphons in a graphical fashion, where we also showed that an SMS can be synthesised from a strongly resource subnet in an S 3 PR. The author further proved in [13] that each elementary siphon can be synthesised from an elementary resource circuit, whereas a dependent siphon can be synthesised from a compound resource circuit…”

Section: Graphical Search Of Elementary Siphonsmentioning

confidence: 86%

Modified definition of characteristic P-vector for elementary siphons in a class of Petri nets

Chao

2010

IET Control Theory &Amp; Applications

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Section: Graphical Search Of Elementary Siphonsmentioning

confidence: 86%

Modified definition of characteristic P-vector for elementary siphons in a class of Petri nets

Chao

2010

IET Control Theory &Amp; Applications

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“…They assume that the siphon constructed from each resource circuit is elementary and proposed a polynomial algorithm to compute elementary siphons. The work by Chao 219 develops a polynomial algorithm to find elementary siphons, which also constructs all SMSs on the way. The reason is that in the method proposed by Li and Zhou, 269 a linear algebraic expression must be established for each dependent siphon, which implies that all SMSs must be located.…”

Section: Elementary Siphons Computationmentioning

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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“…In refs (Chao 2007b(Chao , 2008a we show that strict minimal siphon (SMS) can be calculated from strongly connected resource subnets. New types (such as control siphons) of SMS can be calculated from strongly connected control subnets formed by control places (considered as a new type of resources).…”

Section: Types Of Strict Minimal Siphonmentioning

confidence: 99%

“…Using the MIP (mixed integer programming) method (Chu and Xie 1997) the unmarked siphons obtained may not be in this order and hence some of them may be redundant. SMS can be calculated based on the Handle-Construction Procedure in refs (Chao 2007b(Chao , 2008a.…”

Section: Types Of Strict Minimal Siphonmentioning

confidence: 99%

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Controllability of control and mixture weakly dependent siphons in S³PR

Hong

Chao

2013

International Journal of Systems Science

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Deadlocks in a flexible manufacturing system modelled by Petri nets arise from insufficiently marked siphons. Monitors are added to control these siphons to avoid deadlocks rendering the system too complicated since the total number of monitors grows exponentially. Li and Zhou propose to add monitors only to elementary siphons while controlling the other (strongly or weakly) dependent siphons by adjusting control depth variables. To avoid generating new siphons, the control arcs are ended at source transitions of process nets. This disturbs the original model more and hence loses more live states. Negative terms in the controllability make the control policy for weakly dependent siphons rather conservative. We studied earlier on the controllability of strongly dependent siphons and proposed to add monitors in the order of basic, compound, control, partial mixture and full mixture (strongly dependent) siphons to reduce the number of mixed integer programming iterations and redundant monitors. This article further investigates the controllability of siphons derived from weakly 2-compound siphons. We discover that the controllability for weakly and strongly compound siphons is similar. It no longer holds for control and mixture siphons. Some control and mixture siphons, derived from strongly 2-compound siphons are not redundant -no longer so for those derived from weakly 2-compound siphons; that is all control and mixture siphons are redundant. They do not need to be the conservative one as proposed by Li and Zhou. Thus, we can adopt the maximally permissive control policy even though new siphons are generated.

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Incremental approach to computation of elementary siphons for arbitrary simple sequential processes with resources

Cited by 30 publications

References 6 publications

Modified definition of characteristic P-vector for elementary siphons in a class of Petri nets

Modified definition of characteristic P-vector for elementary siphons in a class of Petri nets

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

Controllability of control and mixture weakly dependent siphons in S³PR

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Incremental approach to computation of elementary siphons for arbitrary simple sequential processes with resources

Cited by 30 publications

References 6 publications

Modified definition of characteristic P-vector for elementary siphons in a class of Petri nets

Modified definition of characteristic P-vector for elementary siphons in a class of Petri nets

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

Controllability of control and mixture weakly dependent siphons in S3PR

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Controllability of control and mixture weakly dependent siphons in S³PR