Optimisation de la méthode de synthèse de commande par supervision des systèmes à événements discrets basée sur les invariants de marquage

Abstract : The discrete event system (DES) control theory was initially developed using finite state automata, with the aim of guaranteeing a priori operation in conformity with the specifications which are generally decline as forbidden states.The automata represent a powerful modeling formalism of the DESs, despite their great sensitivity to the combinatorial explosion problem of the number of states. This disadvantage is minimized when the modeling is carried out by the Petri nets (PN). However, this advantage in concision is counterbalanced by the loss of the optimality of the results provided by the automata. However, among many methods of synthesis of supervisory control by PN, the invariants method is the most used for the However, among many methods of synthesis of supervisory control by PN, the invariants method is the most used for computing the controller. Unfortunately, this approach does not generally guarantee an optimal solution if it is used in a conventional way, and especially in the case where the synchronization of the PNs of the DES is carried out by uncontrollable transitions. The solution consists in identifying the admissible constraints suitable for the synthesis of the maximum permissive (optimal) controller. We proposed a fusion approach based on the Kumar algorithm to determine the constraints related to the forbidden boundary states, for computing the controller. But the need to explore the state space of the PN, namely the marking graph, led us to represent the marking graph by its transition function, namely, the transition matrix. The coding of the elements of the matrix, according to the DES specification enabled us to identify the states constituting the hyperplane (decision function) and the appropriate boundary states
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Mohaman Gonza, Laurent Bitjoka. Optimisation de la méthode de synthèse de commande par supervision des systèmes à événements discrets basée sur les invariants de marquage. 2017. 〈hal-01590999〉

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