Asynchronous Diagnosability Enforcement in Discrete Event Systems Based on Supervisory Control

An asynchronous fault diagnosis problem consists in determining the occurrence of faults in a plant under the condition that a diagnosis agent, i.e., a diagnoser, is activated asynchronously with the plant. Asynchronous diagnosability is a property implying that any fault in a plant can be detected by observing a finite number of observations in the case of asynchronous activation of the diagnoser and the plant. This article studies the problem of asynchronous diagnosability enforcement in discrete event systems (DESs) based on supervisory control theory, i.e., to develop a supervisor for an asynchronously undiagnosable plant such that the asynchronous diagnosability of the closed-loop system is guaranteed. First, the classical definition of asynchronous diagnosability is generalized to nonlive systems since a supervisor may introduce deadlocks in a plant even if it is originally live. We then propose a structure called an asynchronous-quiescent diagnoser that is used for both online asynchronous diagnosis and asynchronous diagnosability determination. Finally, for a plant that is asynchronously undiagnosable, we develop a supervisor to enforce the asynchronous diagnosability based on its asynchronous-quiescent diagnoser.