Detectability of Discrete Event Systems

In this note, we investigate the detectability problem in discrete event systems. We assume that we do not know initially which state the system is in. The problem is to determine the current and subsequent states of the system based on a sequence of observations. The observation includes partial ev...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 52; no. 12; pp. 2356 - 2359
Main Authors: Shu, Shaolong, Lin, Feng, Ying, Hao
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.12.2007
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Applied sciences
Automatic control
Biomedical equipment
Computer science; control theory; systems
Construction
Control systems
Control theory. Systems
Detectability
Diagnosis
Discrete event systems
Event detection
Exact sciences and technology
Failure
Feedback control
Medical services
Modelling and identification
Observability
Observers
State estimation
Sufficient conditions
Supervisory control
Closed feedback
discrete event systems
Observer
Detectability
Feedback regulation
System identification
State estimation
Observability
Fault diagnostic
Discrete event system
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:In this note, we investigate the detectability problem in discrete event systems. We assume that we do not know initially which state the system is in. The problem is to determine the current and subsequent states of the system based on a sequence of observations. The observation includes partial event observation and/or partial state observation, which leads to four possible cases. We further define four types of detectabilities: strong detectability, (weak) detectability, strong periodic detectability, and (weak) periodic detectability. We derive necessary and sufficient conditions for these detectabilities. These conditions can be checked by constructing an observer, which models the estimation of states under different observations. The theory developed in this note can be used in feedback control and diagnosis. If the system is detectable, then the observer can be used as a diagnoser to diagnose the failure states of the system.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2007.910713