Algebraic Structures in Interpreted Petri nets

Abstract

Modern Discrete Events Systems (SED) such as Manufacturing systems, Transport and Logistic system, among many others, are very large and complex. The bottom-up modeling methodologies based on building basic modules (either in Finite Automata (FA) or Petri nets (PN)) and then merging them using synchronous and permissive products result insufficient (the derived models are large and unreadable). To cope this problem, this paper introduces a modeling methodology based on the novel synchronous product, denotes as "∥". This single product subsumes the previously reported synchronous and permissive products, and it is capable to handle large system in a formal yet efficient way. The main advantage of this new product deals in the fact that it is an associative and commutative operator in the class of Compositional State Machines (CSM). Moreover, (CSM,∥) forms a moniod. Furthermore, by defining a partial order relation on the CSM set, a lattice is found. This structure is relevant since the resulting meet operation provides the common subsystems of a couple of systems, and the join operation represents how subsystems build a larger system. Finally, the purpose of this modelling methodology is twofold, on the one hand the model of the system is easy to follow and can be displayed in a Human-Machine Interface (HMI), on the other hand it can be used for analysis and control purposes.