Fault Diagnosis in Discrete-Event Systems with Incomplete Models: Learnability and Diagnosability

Most model-based approaches to fault diagnosis of discrete-event systems require a complete and accurate model of the system to be diagnosed. However, the discrete-event model may have arisen from abstraction and simplification of a continuous time system, or through model building from input-output data. As such, it may not capture the dynamic behavior of the system completely. In a previous paper, we addressed the problem of diagnosing faults given an incomplete model of the discrete-event system. We presented the learning diagnoser which not only diagnoses faults, but also attempts to learn missing model information through parsimonious hypothesis generation. In this paper, we study the properties of learnability and diagnosability. Learnability deals with the issue of whether the missing model information can be learned, while diagnosability corresponds to the ability to detect and isolate a fault after it has occurred. We provide conditions under which the learning diagnoser can learn missing model information. We define the notions of weak and strong diagnosability and also give conditions under which they hold.