A New Approach for Verification of Delay Co-observability of Discrete-Event Systems

In decentralized networked supervisory control of discrete-event systems (DESs), the local supervisors observe event occurrences subject to observation delays to make correct control decisions. Delay co-observability describes whether these local supervisors can make sufficient observations. In this article, we provide an efficient way to verify delay co-observability. For each controllable event, we partition the specification language into a finite number of sets such that strings in different sets have different lengths. For each set, we construct a verifier to check if delay co-observability holds for the controllable event. The computational complexity of the proposed approach is polynomial with respect to the number of states, the number of events, and the upper bounds on observation delays and only exponential with respect to the number of local supervisors. It has a lower complexity order than the existing approaches. In addition, we investigate the relationship between the decentralized supervisory control of networked DESs and the decentralized fault diagnosis of networked DESs and show that delay
$K$
-codiagnosability is transformable to delay co-observability. Thus, techniques for the verification of delay co-observability can be leveraged to verify delay
$K$
-codiagnosability.