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Conception des systèmes de production à l'aide des réseaux de Petri : vérification incrémentale des propriétés qualitatives

Abstract : In this work, we are interested in the production systems design based on Petri nets. The objective is to check the qualitative properties of the system in a step by step design process. An efficient behavior of un system needs an appropriate design. Thus, the Petri net model of the system should possess desirable qualitative properties, namely : consistency, conservativeness, structural boundedness, repititiviness, deadlock-freeness and liveness, and so on. We consider a step design process which corresponds to a real life situation. The action taken at each step consists of adding places and/or transitions to an existing model, or of integrating several existing models by merging places and/or transistions. We examine the problem from the point of view of an engineer who designs a model and who wants to know, at each cach step of the design process, if his model preserves the required properties. The results presented in this thesis provide a theorical basis for the development of a tool devoted to this kind of tests. The theoretical results presented in this work allow to perform these checkings by only considering a part of the whole model. Using linear algebraic methods, we propose necessary and/or sufficient conditions to preserve consistency, conservativeness, structural boundedness and repetitiviness. Deadlock-freeness and liveness are checked using siphons and traps. We prove theorems that give the evolution of the siphon and trap bases from step to step in the design process. These results allow to develop algorithms to find out the siphon and trap bases. We define the notion of fatal siphon from which we establish necessary and/or sufficient conditions for the deadlock-freeness of any ordinary Petri nets and the liveness of asymmetric nets and event graphs with shared resource places. We show that the absence of fatal siphons can be checked out by a linear program
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Feng Chu. Conception des systèmes de production à l'aide des réseaux de Petri : vérification incrémentale des propriétés qualitatives. Autre. Université Paul Verlaine - Metz, 2015. Français. ⟨NNT : 1995METZ007S⟩. ⟨tel-01776876⟩

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