Diagnosability of discrete-event systems

Abstract

Fault detection and isolation is a crucial and challenging task in the automatic control of large complex systems. We propose a discrete-event system (DES) approach to the problem of failure diagnosis. We introduce two related notions of diagnosability of DES's in the framework of formal languages and compare diagnosability with the related notions of observability and invertibility. We present a systematic procedure for detection and isolation of failure events using diagnosers and provide necessary and sufficient conditions for a language to be diagnosable. The diagnoser performs diagnostics using online observations of the system behavior; it is also used to state and verify off-line the necessary and sufficient conditions for diagnosability. These conditions are stated on the diagnoser or variations thereof. The approach to failure diagnosis presented in this paper is applicable to systems that fall naturally in the class of DES's; moreover, for the purpose of diagnosis, most continuous variable dynamic systems can be viewed as DES's at a higher level of abstraction. In a companion paper [20], we provide a methodology for building DES models for the purpose of failure diagnosis and present applications of the theory developed in this paper.

Fault detection for discrete event systems using Petri nets with unobservable transitions

“…In the context of automata Sampath et al [15,16] propose an approach to failure diagnosis where the system is modeled as a nondeterministic automaton in which the failures are treated as unobservable events. In [15] they provide a definition of diagnosability in the framework of formal languages and establish necessary and sufficient conditions for diagnosability. Moreover, in [14] Sampath et al present an integrated approach to control and diagnosis.…”

Opacity of discrete event systems and its applications

“…Controllability [20] and observability together provide a necessary and sufficient condition for the existence of a supervisor. Diagnosability deals with fault diagnosis [23]. A discrete event system is said to be diagnosable if any failure can be diagnosed after finite number of occurrences of events.…”

Distributed Unfolding of Petri Nets

“…Although it has an important intersection with diagnosis, control is a clearly distinct problem, not addressed by the present article. Diagnosis can be approached via the construction of finite automata, the diagnosers, detailed in [19]; the input of a diagnosis procedure is the language of observed sequences and its output is the language of behaviours that explain the observations. Communication among diagnosers allows for a decentralised diagnosis, in which different diagnoses are proposed by various local diagnosers and then merged to filter out incompatible local views (see, e.g., [6,16,5]).…”