Observability and diagnosability of finite state systems: a unifying framework

TL;DR

This paper introduces a comprehensive framework for analyzing observability and diagnosability in finite state systems, enabling precise characterization, comparison, and delay estimation for fault detection and state reconstruction.

Contribution

It unifies various existing notions of observability and diagnosability within a single framework, providing new conditions and metrics for delay and precision estimation.

Findings

Framework characterizes observability and diagnosability with respect to a critical set.

Provides conditions for delay estimation in fault detection.

Enables comparison of different existing notions in the literature.

Abstract

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.