This paper focuses on the problem of estimating the marking of an unlabeled P-time Petri net with partial information modeled by unobservable transitions. The proposed approach is based on a novel state observer synthesis method under partial observation. A procedure that, given a sequence of observable transitions with their firing time instants, allows to determine the set of markings consistent with the considered observation is given. The method relies on the feasibility in time (called schedulability) of particular firing sequences, namely the candidates firing sequences. Moreover, although time is taken into consideration, the proposed technique is not hampered by the state space explosion problem as it relies on the underlying untimed structure of the P-time model considered-the building of the state class graph is not necessary.
International audiencePetri nets are a powerful formalism for the specification and verification of concurrent systems, such as sequential systems and manufacturing systems. To deal with real-time systems whose time issues become essential, different extensions of Petri nets with time have been proposed in the literature. In this paper, a new scheduling and control technique for real-time systems modeled by ordinary P-time Petri nets is proposed. Its goal is to provide a scheduling for a particular firing sequence, without any violation of timing constraints ensuring that no deadline is missed. It is based on the firing instant notion and it consists in determining an inequality system generated for a possible evolution (in terms of a feasible firing sequence for the untimed underlying Petri net) of the model. This system can be used to check reachability problems as well as evaluating the performances of the model considered and determining the associated control for a definite functioning mode and it introduces partial order on the execution of particular events
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