Verification of Delay Co-Observability for Discrete Event Systems

Abstract

In this paper, we investigate how to verify delay co-observability for a given discrete event system and its specification language. Delay co-observability is introduced to solve the decentralized nonblocking networked control problem for discrete event systems under nondeterministic communication delays in our previous paper. We first define a set of indistinguishable string collections and transform the verification problem of delay co-observability to the problem of checking if all of the indistinguishable string collections are valid or not. We then construct a set of verifiers to track all of these string collections. Checking if all of the indistinguishable string collections are valid or not can be done by checking if the states in these verifiers are “good” or “bad”. The specification language is delay co-observable if and only if there are no “bad” states in all verifiers. The computational complexity of the proposed algorithm is polynomial with respect to the number of states and events of the system and exponential with respect to the number of local supervisors and the upper bounds on the delays.