Strong Co-Detectability for Labeled Petri Nets and its Enforcement via Additional Sensors

This paper addresses the problem of verifying co-detectability for a labeled Petri net that is observed at multiple observation sites, each with its own observation map. A system is strongly co-detectable if at least one site is able to determine the state of the system uniquely following any long enough sequence of observations. We check strong co-detectability for a labeled Petri net using an approach that exploits the notion of basis markings, which avoids an exhaustive enumeration of all reachable markings of the net. Specifically, a structure called BRG-based co-verifier is exploited for the verification of strong co-detectability. In addition, by employing the proposed BRG-based co-verifier, some rules and relabeling options are provided to identify a new relabeling function such that a system that is not strongly co-detectable becomes strongly co-detectable. Finally, an integer programming problem is formulated to find an optimal relabeling function when considering different relabeling costs on transitions.