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Séparation des états du graphe de marquages d'un réseau de Petri pour la commande par supervision des systèmes à événements discrets

Abstract : The markings graph is usually large so that we can identify in the simple and efficient way the suitable set of states for control synthesis of discrete event systems. Moreover, the combinatorial explosion problem inherent in control theory is present in the methods of synthesis based on the marking graph. Among these methods, the method of invariants markings which is the most used cannot guarantee the optimality of the results if and only if the suitable set of linear constraints links to forbidden states or markings supplied to it. To find such a suitable set of constraints, the state space of the markings graph of Petri net modeling the discrete event system must be separated. This paper presents an approach of separation of accessible markings graph into sets of forbidden states and allowed states. The markings graph is represented by his codified transition function matrix. This separation is defined by a decision function that characterizes the set of border or criticism states. This set constitutes the hyperplane separation that can be used to determine bijectively admissible constraints necessary for the synthesis of supervision by the method of invariants markings.
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https://hal.inria.fr/hal-01485637
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Submitted on : Thursday, March 9, 2017 - 11:04:32 AM
Last modification on : Wednesday, November 3, 2021 - 5:07:59 AM

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Mohaman Gonza, Laurent Bitjoka, Hassane Alla. Séparation des états du graphe de marquages d'un réseau de Petri pour la commande par supervision des systèmes à événements discrets. 2016. ⟨hal-01485637⟩

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