A Structure-Modification-Based Petri Net Modeling and Reachability Analysis Method for Automated Manufacturing Systems

Due to their graphical representation and capability for property analysis, Petri nets (PNs) have been widely used in developing automated manufacturing systems (AMS). When doing so, it is important to perform their state reachability analysis and verify their functionality. The most common approach is to traverse a reachability tree of their PN models. However, it has the problem of state space explosion. A way to determine a state’s reachability is to find a firing sequence (FS) that corresponds to nonnegative integer solutions (NISs) of a state equation. Our prior work has given an algorithm to decide the existence of FS corresponding to an NIS in polynomial time. Yet it is impossible to decide the reachability of a marking given an infinite number of NISs of a state equation. This work studies the relationship between the PN model and NIS count of any state equation. An innovative method is proposed to modify a PN structure such that, for any initial state and destination one, its state equation has no more than one NIS. Given a PN model of an AMS, by analyzing the relationship between its properties and the modified one’s, we have that the proposed method can maintain the functionality of the modeled AMS. As a result, by using the modified PN as the AMS’s final model, the reachability of any marking can be determined in polynomial time, which can be viewed as a breakthrough result in the field of PN analysis. The proposed method is illustrated via case studies. Note to Practitioners—Petri nets (PNs) are established formal tools with extensive application in the modeling and analysis of automated manufacturing systems (AMS). Reachability is to determine whether an AMS can reach a state from an initial one, which is crucial for ensuring system robustness. However, for PN-based AMS, existing methods have difficulty in determining the reachability of an arbitrary state due to excessive computational complexity. This research introduces a novel reachability-decidable PN modeling method, where the structure of the PN is modified while preserving the functionality of the modeled system. Consequently, the reachability of any marking can be determined in polynomial time by employing a state-equation-based method. The proposed approach avoids exhaustive state enumeration, resulting in significant time and computational resource savings. It is important in promoting PN’s industrial applications.