Path detectability verification for time-dependent systems with application to flexible manufacturing systems

This paper addresses the path detectability verification problem for time-dependent systems modeled by time labeled Petri nets (TLPNs). To capture the information precisely, it may not be sufficient to estimate the current state by resorting to the partial system observation, and it is usually crucial to decide the path of a system to reach the current state. Path detectability characterizes a time-dependent system whose current state and the corresponding path can be uniquely determined after a real-time observation (RTO). Revised state class graphs (RSCGs) are proposed to capture the time information for the evolution of the RTO in a TLPN system. We demonstrate the time information overlap problem in the RSCG, i.e., several paths are associated with the same observable events and the same time instants, which leads to such paths that cannot be distinguished. The nodes required to be computed in the proposed RSCGs are always less or equal to those of the modified state class graphs reported in the literature, since the enumeration of all the states is avoided. Based on the RSCG, an RSCG observer is formulated to address the time information overlap problem and capture the number of such paths in the TLPN system. The efficiency analysis of this verification method is provided. In this paper, the results are applied to a real production system, exposing the practical value of the reported method.