Optimal Legal Firing Sequence of Petri Nets Using Linear Programming

Tarek, Ahmed; Lopez-Benitez, N.

doi:10.1023/b:opte.0000013633.35184.6d

Cited by 21 publications

(3 citation statements)

References 8 publications

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“…By considering the method in [9], this section finds legal transition firing sequences that lead the system from the initial state to the destination state without violating the specified control specifications by solving an integer linear programming model formulated by utilizing the fact that at any reachable marking, at which there exists at least a transi tion that is enabled. Once the legal sequences are obtained, monitors can be used to enforce the control specifications via disabling the illegal transitions sequences.…”

Section: Legal Transition Firing Sequencesmentioning

confidence: 99%

A monitor solution to enforce legal transition firing sequences problems by using Petri nets

Gao

Wang

et al. 2014

2014 IEEE International Conference on Automation Science and Engineering (CASE)

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This paper focuses on supervisory control of a class of discrete event systems with known initial and desti nation states, whose evolution conforms to a set of specified linear or non-linear constraints. A supervisor is designed, which supervises the considered system to evolve and finally to reach the destination state with minimal costs without violating the specified constraints. A partial structure of the Petri net model of a system is first created by the constraints. Then, we find the destination state under the constraints by a search algorithm with least cost. A legal transition firing sequence can be found by solving integer programming problems with the constraints of the created model and the result of the search algorithm. Otherwise, a more exhaustive model is made under the limit of the constraints. Then, a set of control places is used to implement the transition sequence by introducing a set of complementary transitions. A mental game example is used to demonstrate the proposed approaches.

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Section: Legal Transition Firing Sequencesmentioning

confidence: 99%

A monitor solution to enforce legal transition firing sequences problems by using Petri nets

Gao

Wang

et al. 2014

2014 IEEE International Conference on Automation Science and Engineering (CASE)

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“…For such nets, the state equation represents all the reachable states if the initial marking M 0 satisfies some constraints. Further efforts have been made for extending the validity of the state equation to more classes of nets [28].…”

Section: ⊓ ⊔mentioning

confidence: 99%

A graphical formalism for mixed multi-unit combinatorial auctions

Giovannucci

Cerquides

Endriss

et al. 2009

Auton Agent Multi-Agent Syst

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Mixed Multi-Unit Combinatorial Auctions are auctions that allow participants to bid for bundles of goods to buy, for bundles of goods to sell, and for transformations of goods. The intuitive meaning of a bid for a transformation is that the bidder is offering to produce a set of output goods after having received a set of input goods. To solve such an auction the auctioneer has to choose a set of bids to accept and decide on a sequence in which to implement the associated transformations. Mixed auctions can potentially be employed for the automated assembly of supply chains of agents. However, mixed auctions can be effectively applied only if we can also ensure their computational feasibility without jeopardising optimality. To this end, we propose a graphical formalism, based on Petri nets, that facilitates the compact represention of both the search space and the solutions associated with the winner determination problem for mixed auctions. This approach allows us to dramatically reduce the number of decision variables required for solving a broad class of mixed auction winner determination problems. An additional major benefit of our graphical formalism is that

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“…The optimization of performance and cost for DES has been frequently considered with PN-based approaches. 23,24 The pioneer approaches were based on an exhaustive search in reachability graph, and one of the main difficulties is that these approaches require the computation of the entire graph that prevents their application to large systems because the exhaustive expansion is exp-time and exp-space hard. Consequently, a lot of works have been devoted to compute partial expansions of the reachability graph in order to reduce the computational complexity by removing the less promising branches of the graph.…”

Section: Introductionmentioning

confidence: 99%

Algorithms of reduced complexity to design control sequences for untimed Petri nets in varying and uncertain environments

Lefebvre

2018

Proceedings of the Institution of Mechanical Engineers, Part I:

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Petri nets have been widely used for the modelling, analysis, control and optimization of discrete event systems with shared resources in the domains of engineering. This article concerns the design of control sequences for such systems modelled with untimed Petri nets. The aim of the controller is to incrementally compute sequences of transition firings with minimal size. Such sequences aim to move the marking from an initial value to a reference value. The resulting trajectory must avoid some forbidden markings and limit as possible the exploration of non-promising branches. For this purpose, the approach explores a small part of the reachability graph in the neighbourhood of the current marking. Then from the explored markings, it estimates a distance to the reference. The main contributions are (a) to reduce the explored part of the reachability graph according to a double limitation in breadth and in depth in order to provide solutions with a low computational effort; (b) to provide conditions to ensure the converge and optimality of the proposed algorithms and derive necessary and sufficient conditions for reachability; and (c) to include the firing sequence design in a global control schema suitable for reactive scheduling problems in uncertain and perturbed environments. The main application concerns deadlock-free scheduling problems in the domain of flexible manufacturing systems, but the approach is also applicable for systems in computer science and transportation.

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Optimal Legal Firing Sequence of Petri Nets Using Linear Programming

Cited by 21 publications

References 8 publications

A monitor solution to enforce legal transition firing sequences problems by using Petri nets

A monitor solution to enforce legal transition firing sequences problems by using Petri nets

A graphical formalism for mixed multi-unit combinatorial auctions

Algorithms of reduced complexity to design control sequences for untimed Petri nets in varying and uncertain environments

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