Observer design for untimed continuous Petri nets

Continuous Petri nets (conPNs) are an approximation of (discrete) Petri nets (PNs) introduced to cope with the state explosion problem typical of discrete event systems. We consider a free-labeled Petri net model and assume that certain transitions, including all that model faulty behaviors are unobservable, i.e., they are labeled with the empty word. We show how to design a marking observer that consists in a linear algebraic characterization of the set of markings that is consistent with a given observation. For some subclasses of nets the results can be extended to the discrete case where the computational complexity is much bigger than the one of continuous systems.