Diagnosability of discrete-event systems with uncertain observations

Diagnosability is the property that a Discrete-Event System (DES) exhibits if every fault can be detected and isolated within a finite number of (observable) events that have taken place after its occurrence. In the literature, diagnosability of DESs relies on the availability of a certain observation, which equals the sequence of observable events that have taken place in the DES. But can diagnosability be achieved even if the observation is uncertain? The present paper provides an answer to this question when the observation is temporally or logically uncertain, that is, when the order of the observed events or their (discrete) values are partially unknown. The original notion of compound observable event enables a smooth extension of both the definition of DES diagnosability in the literature and the twin plant method to check such a property. The intuition is to deal with a compound observable event the same way as with a single event. In case a DES is diagnosable even if its observation is uncertain, the diagnosis task can be performed (without any loss in the ability to identify every fault) although the available measuring equipment cannot get a certain observation.