2016/08/10 by Elena De Santis, De Santis, Elena, Maria Domenica Di Benedetto +1
Computer Science · Engineering · Mathematics · #93B99 #Advanced Control Systems Optimization #FOS: Mathematics #Fault Detection and Control Systems #Optimization and Control (math.OC) #Petri Nets in System Modeling #math.OC #msc:93B99
paper · pdf · doi:10.48550/arxiv.1608.03195
25 pages, 11 figures
openalex publication_date 2016/08/10 · arxiv created 2016/11/25 · arxiv updated 2016/11/28 · openalex created_date 2022/08/13 · openalex updated_date 2026/07/28
In this paper, a general framework is proposed for the analysis and characterization of observability and diagnosability of finite state systems. Observability corresponds to the reconstruction of the system's discrete state, while diagnosability corresponds to the possibility of determining the past occurrence of some particular states, for example faulty states. A unifying framework is proposed where observability and diagnosability properties are defined with respect to a critical set, i.e. a set of discrete states representing a set of faults, or more generally a set of interest. These properties are characterized and the involved conditions provide an estimation of the delay required for the detection of a critical state, of the precision of the delay estimation and of the duration of a possible initial transient where the diagnosis is not possible or not required. Our framework makes it possible to precisely compare some of the observability and diagnosability notions existing in the literature with the ones introduced in our paper, and this comparison is presented.