Fault Diagnosis of Discrete-Event Systems under Non-Deterministic Observations with Output Fairness

TL;DR

This paper introduces output-fair diagnosability for discrete-event systems, addressing non-deterministic observations with intermittent loss, and provides a verification approach that better models real-world sensor behaviors.

Contribution

It proposes a new output-fair diagnosability concept and an effective method for its verification, improving fault diagnosis under non-deterministic observation conditions.

Findings

Output-fair diagnosability is weaker than standard diagnosability.

The approach effectively captures intermittent observation loss.

Verification method is practical for real-world systems.

Abstract

In this paper, we revisit the fault diagnosis problem of discrete-event systems (DES) under non-deterministic observations. Non-deterministic observation is a general observation model that includes the case of intermittent loss of observations. In this setting, upon the occurrence of an event, the sensor reading may be non-deterministic such that a set of output symbols are all possible. Existing works on fault diagnosis under non-deterministic observations require to consider all possible observation realizations. However, this approach includes the case where some possible outputs are permanently disabled. In this work, we introduce the concept of output fairness by requiring that, for any output symbols, if it has infinite chances to be generated, then it will indeed be generated infinite number of times. We use an assume-guarantee type of linear temporal logic formulas to formally describe this assumption. A new notion called output-fair diagnosability (OF-diagnosability) is proposed. An effective approach is provided for the verification of OF-diagnosability. We show that the proposed notion of OF-diagnosability is weaker than the standard definition of diagnosability under non-deterministic observations, and it better captures the physical scenario of observation non-determinism or intermittent loss of observations.