On liveness and controlled siphons in Petri nets

Barkaoui, Kamel; Pradat-Peyre, Jean-François

doi:10.1007/3-540-61363-3_4

Cited by 142 publications

(172 citation statements)

References 3 publications

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“…234 A net is said to be completely controllable if any marking is reachable from any other marking. 34 In an ordinary Petri net, a siphon is said to be controlled if it cannot be unmarked at any reachable marking.…”

Section: Controllability Conditions Of Siphonsmentioning

confidence: 99%

“…Let (N , M 0 ) be an ordinary net and P be the set of its siphons. 31,234 The net is deadlock-free if 8S 2 P, 8M 2 R(N, M 0 ), M(S).0.…”

Section: Controllability Conditions Of Siphonsmentioning

confidence: 99%

“…31,234 Definition 2. A siphon S is said to be controlled in an ordinary Petri net system (N , M 0 ) if 8M 2 R(N, M 0 ), M(S).0.…”

Section: Corollarymentioning

confidence: 99%

“…215 Li and Zhao extend such a result to a class of generalized nets in the work by Li and Zhao 243 on the basis of the max-controlled condition of siphons. 234 However, it suffers from the computational complexity and behavioral permissiveness issues as in this 243 policy since the computation of elementary siphons relies on a complete siphon enumeration.…”

Section: Elementary Siphon-based Approachesmentioning

confidence: 99%

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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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Section: Controllability Conditions Of Siphonsmentioning

confidence: 99%

“…Let (N , M 0 ) be an ordinary net and P be the set of its siphons. 31,234 The net is deadlock-free if 8S 2 P, 8M 2 R(N, M 0 ), M(S).0.…”

Section: Controllability Conditions Of Siphonsmentioning

confidence: 99%

“…31,234 Definition 2. A siphon S is said to be controlled in an ordinary Petri net system (N , M 0 ) if 8M 2 R(N, M 0 ), M(S).0.…”

Section: Corollarymentioning

confidence: 99%

Section: Elementary Siphon-based Approachesmentioning

confidence: 99%

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

Hou

Barkaoui

2017

Advances in Mechanical Engineering

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“…The key reason is that the Petri net modeling framework might not be able to express the MPLE property for general process-resource nets; as a result, the problem of MPLE control synthesis based on siphon analysis in nonordinary nets has not been well-resolved yet [13]. In [1], the "max-controlled-siphon-property" is proposed; however, siphon-based control synthesis by enforcing this property is not maximally permissive in general.…”

Section: Introductionmentioning

confidence: 99%

Optimal Liveness-Enforcing Control for a Class of Petri Nets Arising in Multithreaded Software

Liao

Lafortune

Reveliotis

et al. 2013

IEEE Trans. Automat. Contr.

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Abstract-We investigate the synthesis of optimal livenessenforcing control policies for Gadara nets, a special class of Petri nets that arises in the modeling of the execution of multithreaded computer programs for the purpose of deadlock avoidance. We consider maximal permissiveness as the notion of optimality. Deadlock-freeness of a multithreaded program corresponds to liveness of its Gadara net model. We present a new control synthesis algorithm for liveness enforcement of Gadara nets that need not be ordinary. The algorithm employs structural analysis of the net and synthesizes monitor places to prevent the formation of a special class of siphons, termed resource-induced deadlymarked siphons. The algorithm also accounts for uncontrollable transitions in the net in a minimally restrictive manner. The algorithm is generally an iterative process and converges in a finite number of iterations. It exploits a covering of the unsafe states that is updated at each iteration. The proposed algorithm is shown to be correct and maximally permissive with respect to the goal of liveness enforcement.

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Deadlock Control for a Class of Generalized Petri Nets Based on Proper Resource Allocation

Hou¹,

Zhao²,

Liu³

2014

Asian Journal of Control

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This article develops a deadlock prevention policy for a class of generalized Petri nets, namely G‐systems, which can model flexible manufacturing systems with machining, assembly, and disassembly operations. In this research, a polynomial complexity control policy for non‐blocking supervisors is established by properly adjusting resource allocation. First, a set of linear inequality constraints is derived with respect to different resource requirements such that the allocation of the system resources to various requesting processes can be appropriately restricted, that is, the resulting system has no deadlock state by imposing monitors on operation places. Moreover, an algorithm is proposed to identify the redundant constraints such that structurally simple liveness‐enforcing net supervisors can be obtained. Compared with existing polices, the proposed method can usually lead to a suboptimal supervisor with high computational efficiency. Finally, a flexible manufacturing system example is utilized to demonstrate the proposed method.

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On liveness and controlled siphons in Petri nets

Cited by 142 publications

References 3 publications

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

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

Optimal Liveness-Enforcing Control for a Class of Petri Nets Arising in Multithreaded Software

Deadlock Control for a Class of Generalized Petri Nets Based on Proper Resource Allocation

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