Maximally permissive supervisor synthesis based on a new constraint transformation method

Luo, Jiliang; Shao, Hui; Nonami, Kenzo; Jin, Fujiang

doi:10.1016/j.automatica.2012.02.002

Cited by 28 publications

(35 citation statements)

References 17 publications

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“…A fundamental result in Luo et al (2012), from which all subsequent results are derived, is Theorem 2 that shows how an inadmissible GMEC (w, k) can be transformed into a disjunction of equivalent GMECs  (W ).…”

Section: Counterexample For Theorem 2 In Luo Et Al (2012)mentioning

confidence: 99%

“…The notion of equivalence used in Luo et al (2012) implies that the sets of admissible markings of the original and transformed constraints are identical, i.e., A (w,k) …”

Section: Counterexample For Theorem 2 In Luo Et Al (2012)mentioning

confidence: 99%

“…Since w T · C (·, t 5 ) = 1, by applying the Uncontrollable Transition Gain Transformation (UTGT, see Luo et al, 2012 for its definition) function we have:…”

Section: Counterexample For Theorem 2 In Luo Et Al (2012)mentioning

confidence: 99%

“…In the rest of the paper, for consistency we use the term GMEC to refer to the linear constraint in Luo et al (2012).…”

mentioning

confidence: 99%

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Comments on “Maximally permissive supervisor synthesis based on a new constraint transformation method” [Automatica 48 (2012), 1097–1101]

Giua

2015

Automatica

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Section: Counterexample For Theorem 2 In Luo Et Al (2012)mentioning

confidence: 99%

“…The notion of equivalence used in Luo et al (2012) implies that the sets of admissible markings of the original and transformed constraints are identical, i.e., A (w,k) …”

Section: Counterexample For Theorem 2 In Luo Et Al (2012)mentioning

confidence: 99%

“…Since w T · C (·, t 5 ) = 1, by applying the Uncontrollable Transition Gain Transformation (UTGT, see Luo et al, 2012 for its definition) function we have:…”

Section: Counterexample For Theorem 2 In Luo Et Al (2012)mentioning

confidence: 99%

“…In the rest of the paper, for consistency we use the term GMEC to refer to the linear constraint in Luo et al (2012).…”

mentioning

confidence: 99%

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Comments on “Maximally permissive supervisor synthesis based on a new constraint transformation method” [Automatica 48 (2012), 1097–1101]

Giua

2015

Automatica

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“…A future topic is to reduce the structural complexity of the proposed supervisors. Another future work is to extend this work to design Petri net supervisors to enforce nonlinear constraints for net models with uncontrollable transitions [29,25,26].…”

Section: Discussionmentioning

confidence: 99%

On the enforcement of a class of nonlinear constraints on Petri nets

et al. 2015

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This paper focuses on the enforcement of nonlinear constraints in Petri nets. First, a supervisory structure is proposed for a nonlinear constraint. The proposed structure consists of added places and transitions. It controls the transitions in the net to be controlled only but does not change its states since there is no arc between the added transitions and the places in the original net. Second, an integer linear programming model is proposed to transform a nonlinear constraint to a minimal number of conjunctive linear constraints that have the same control performance as the nonlinear one. By using a place invariant based method, the obtained linear constraints can be easily enforced by a set of control places. The control places consist to a supervisor that can enforce the given nonlinear constraint. On condition that the admissible markings space of a nonlinear constraint is non-convex, another integer linear programming model is developed to obtain a minimal number of constraints whose disjunctions are equivalent to the nonlinear constraint. Finally, a number of examples are provided to demonstrate the proposed approach.

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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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Maximally permissive supervisor synthesis based on a new constraint transformation method

Cited by 28 publications

References 17 publications

Comments on “Maximally permissive supervisor synthesis based on a new constraint transformation method” [Automatica 48 (2012), 1097–1101]

Comments on “Maximally permissive supervisor synthesis based on a new constraint transformation method” [Automatica 48 (2012), 1097–1101]

On the enforcement of a class of nonlinear constraints on Petri nets

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

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