From fuzzy logic to hybrid Petri nets

This article is about the design and simulation of hybrid dynamic systems modelled by Petri nets without conflict. For this purpose, a fuzzy multi-model is developed that combines a discrete event description and a continuous approximation of the transitions firing. The transitions are characterised by local clocks, firing rates, and starting orders that are described as fuzzy variables. The definition of the fuzzy sets is related to balance parameters that are suitable to represent the discrete and continuous parts of the hybrid Petri nets. In fact, the fuzzy multi-model has two limit behaviours that correspond to T-timed Petri nets and continuous Petri nets with variable speeds when the balance parameters tend either to zero or to infinity. Thus, the spatial distribution of the balance parameters is useful to design and simulate hybrid systems with a unique model.