Coupling Petri nets with deterministic formalisms using co-simulation

Modeling cyber-physical systems is often seen as a highly multi-disciplinary activity. Therefore, efficient methodologies are required to be able to represent environment, plant and control models using the most appropriate formalisms. On the one hand, the Petri net formalism is appropriate to model the environment of a complex cyber-physical system, especially since it inherently supports non-determinism and concurrency. On the other hand, plant models, based on the laws of physics, are often represented using differential equations. In order to produce a relevant simulation of the overall system, the controller, the plant and the environment models are composed. Co-simulation and its industrial standard, the Functional Mock-up Interface, is one such generic technique that allows for the coupling of different executable models. However, coupling a non-deterministic model with other types of models would be equivalent to build the state space of the given composed system, which in some cases is too complex. In this paper we discuss the co-simulation of a Petri net environment model with a system described by causal block diagrams. To reduce the size of the state space explored, we use a constraint language based on automata and trace matching. The approach is applied to the simulation of a simplified train system.