Supervisory Control for Active Diagnosis in Labeled Petri Nets Under Observation and Control Delays

This paper formalizes and addresses the problems of diagnosability verification and enforcement in discrete event systems modeled with labeled Petri nets under observation and control delays. Given a system with observation delays that may disorder the generated observations, delay diagnosability is introduced to characterize whether all faults remain diagnosable under the observation delays. A delayed verifier is established to test the delay diagnosability of the considered system. It is shown that a labeled Petri net under observation delays is diagnosable if and only if the verifier does not contain the confused cycles composed exclusively of pairs of faulty states and normal states. Considering the existence of control delays in the channel between the plant and its supervisor, a delayed supervisor is designed such that the closed-loop system is diagnosable under observation and control delays. Furthermore, the designed supervisor is maximally permissive, i.e., there does not exist another diagnosability enforcement supervisor that is strictly more permissive than the designed one. Examples are presented to demonstrate the proposed method.