Discrete-event state equations and Petri Nets

In this paper we present a novel formulation for the modeling and control of discrete event dynamic systems. This original approach leads to a discrete-event state equations formulation satisfying Kalman axioms, where the state is defined as the sequence of potential events (enabled transitions in terms of Petri net language) forced by the occurrence of state events (free evolution) or by arbitrary input events (forced evolution). The proposed formulation is considered to be very general and appropriate to any discrete event systems. This conviction is supported by the analysis performed by comparing discrete-event state equations with classical discrete-event models like untimed and timed Petri nets, finite-state timed and untimed automata. We show that all these models can be formulated as a sub-class of the discrete-event state equations.