Diagnosability of Discrete Faults with Uncertain Observations

Abstract

This chapter focuses on the discrete event-based transitions of a Hybrid System (HS), that is, it does not deal with the faults inside states, instead it takes into account the faults between states. Hence, the considered model is actually a Discrete-Event System (DES), say the DES underlying the HS, according to which a (type of) fault is one of the discrete events, usually an unobservable one, and a system can be affected by several types of faults. Diagnosability is the property that a 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? This chapter provides an answer to this question when the observation is temporally and/or logically uncertain, that is, when the order of the observed events and/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.