A State-Equation-Based Method to Non-Reachability Analysis of Ordinary Petri Nets With Token-Free Circuit-Based Subnets

Abstract

Petri nets (PNs) can model various event-driven systems well and detect a fault via reachability analysis. Some state-equation-based approaches are designed for only subclasses of PNs with specific structures. A key issue for PNs’ reachability analysis approach based on state equation is that a non-negative integer solution (NIS) to a state equation is necessary but not sufficient for a marking’s reachability. In this paper, we propose a circuit-based subnet. For ordinary Petri nets with token-free circuit-based subnets, we present an algorithm to determine that the state equation has NISs but the marking is non-reachable. We adopt a divide-and-conquer strategy to consider each circuit-based subnet. The proposed method is tested on a PN-based flexible manufacturing system with unreliable resources. When unreliable resources are lost, the non-reachable markings can be determined effectively. Besides, simulations are done, and the results verify the efficiency of the proposed algorithm compared with the reachability-tree-based method.

Keywords

• Petri nets
• reachability analysis
• state equation
• discrete event systems
• flexible manufacturing systems