Observability and diagnosability of finite state systems: A unifying framework

Abstract

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 observabllity and diagnosability notions existing in the literature with the ones introduced in our paper, and this comparison is presented.

Data-Driven Model Discrimination of Switched Nonlinear Systems With Temporal Logic Inference

“…Additionally, to examine the detectability of the models, Tdistinguishability (or T -detectability) is introduced in [13], [22] to find upper bounds on the required time horizon T to distinguish one model from the other, if such a T exists. The notion of T -distinguishability is closely related to the concept of state/mode distinguishability of switched linear systems [23], [24], finite-state systems [25] and switched nonlinear systems [26]. Recently, model discrimination and fault detection using temporal logics specifications have also gained attention.…”

Model Discrimination of Switched Nonlinear Systems With Temporal Logic-Constrained Switching

“…Additionally, to examine the detectability of the models, T -distinguishability (or T -detectability) is introduced in [13], [22] to find upper bounds on the required time horizon T to distinguish one model from the other, if such a T exists. The notion of T -distinguishability is closely related to the concept of state/mode distinguishability of switched linear systems [23], [24], finite-state systems [25] and switched nonlinear systems [26]. Recently, model discrimination and fault detection using temporal logics specifications have also gained attention.…”

Critical Observability for Automata and Petri Nets

“…The state estimation problem is one of the central problems in cyber-physical systems that is of importance, e.g., in safetycritical applications where we need to estimate the current state of a system in the case we have an incomplete information of its behavior. Eminent examples of the state estimation problem are, for example, fault diagnosability [9], [41], [42] asking whether a fault event has occurred and whether its occurrence can be detected within a finite delay, opacity [3], [4], [17], [20], [26], [35], [37], a property related to the privacy and security analysis, asking whether the system reveals its secret to a passive observer (an intruder), detectability [28], [29], [43] asking whether the current and subsequent states can be determined based on observations, marking observability [14] concerning the estimation of the marking of a Petri net, and predictability [12], [13] concerning the future occurrence of a state or of an event.…”

“…De Santis et al [10] introduced the problem for linear switching systems, and Pola et al [25] adapted it for (networks of) finite automata. Critical states are of particular interest in safety-critical applications to model operations that may be unsafe or of a specific interest, where, for instance, the prompt recovery of human errors and device failures are of importance to ensure safety of the system, such as the air traffic management systems [9]- [11]. T Pola et al focused on the algorithmic complexity of checking critical observability for systems modeled as networks of finite automata, using the techniques of decentralization and bisimulation.…”