Continuous Petri nets and hybrid automata: two bisimilar models for the simulation of positive systems

Petri nets (PNs) are a well-known modelling tool for discrete event systems. Continuous PN were introduced in order to avoid the combinatory explosion of the number of states, when considering real life systems. The constant speed continuous Petri net (CCPN) can be used to model discrete events systems; in that case, they constitute an approximation, which is often satisfactory. They can also model positive continuous systems. Hybrid automata (HA) are a less compact and expressive model, but, they can be used to perform powerful analysis. In this paper, we first present deeply the continuous PN and its modelling advantages. Then we present the main contribution of this paper, that is a structural translation algorithm from a CCPN into a HA. The translation algorithm is structural in the sense that it does not depend on the initial marking of the Petri net. We prove the timed bisimilarity between both models.

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