Robustness Analysis of Automated Manufacturing Systems With Unreliable Resources Using Petri Nets

This paper studies the maximally permissive robustness analysis of automated manufacturing systems (AMSs) with unreliable resources in the paradigm of Petri nets (PNs). Two types of robust markings, i.e., strongly robust markings and weakly robust markings, are defined in this paper. We propose robustness equivalence and non-robustness equivalence to characterize the markings that exhibit the same robustness and non-robustness, respectively. Reachability graph (or RG hereafter) is directly used to determine the robustness of markings; however, it is difficult to use in large-scale systems due to formidable computational difficulty. As an alternative, we present a reduced reachability graph (or R(2)G hereafter) based necessary and sufficient condition to check the robustness of markings, in terms of the liveness analysis of markings in R(2)G. We show that all safe markings of an R(2)G correspond to strongly robust markings of the corresponding RG, and deadlock markings as well as their bad markings and livelock markings as well as their bad markings of an R(2)G correspond to non-robust markings and weakly robust markings of the corresponding RG, respectively. Hence, the robustness of markings in an RG can be determined effectively and efficiently through the liveness analysis of markings in the corresponding R(2)G.

Automated summary

This paper investigates the maximally permissive robustness analysis of automated manufacturing systems with unreliable resources using Petri nets. It defines two types of robust markings and introduces the concepts of reachability graph and reduced reachability graph for effectively checking the robustness of markings. The findings show that through the liveness analysis of markings in the reduced reachability graph, the robustness of markings in the corresponding reachability graph can be determined effectively and efficiently.