Comparative analysis of related notions of robust diagnosability of Discrete-Event Systems

In this paper, we revisit the problem of robust diagnosability of Discrete-Event Systems (DES), and present a comparative analysis between the following notions of robust diagnosability existing in the literature: (i) diagnosability of DES subject to permanent sensor failures, assuming that sensors may fail only before the first occurrence of the events they are supposed to record; (ii) diagnosability of DES subject to permanent sensor failures, assuming that sensors may fail at any time; (iii) diagnosability of DES against intermittent loss of observations; (iv) diagnosability of partially observed DES; (v) generalized robust diagnosability. We show that all of the robust diagnosability definitions are particular cases of the generalized robust diagnosability by presenting transformation mechanisms for each one of the analyzed robust diagnosability notions so as to convert it into an equivalent generalized robust diagnosability problem. We also compare the use of projections and masks in the context of language diagnosability and show that there is no loss of generality in using projections in place of masks by presenting a map that transforms the language diagnosability problem with observation mask into an equivalent one with projection.