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A fault detection and isolation filter design method for Markov jump linear parameter‐varying systems
Author(s) -
Gagliardi Gianfranco,
Casavola Alessandro,
Famularo Domenico
Publication year - 2012
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.1261
Subject(s) - control theory (sociology) , fault detection and isolation , markov chain , observer (physics) , linear matrix inequality , residual , filter (signal processing) , filter design , fault (geology) , jump , computer science , mathematics , mathematical optimization , algorithm , statistics , control (management) , physics , quantum mechanics , artificial intelligence , seismology , actuator , computer vision , geology
SUMMARY A fault detection and isolation (FDI) filter design method is proposed for linear parameter‐varying (LPV) systems, which are subject to abrupt changes in their structure. Such a phenomenon is modeled by a finite state Markov chain whose outcome is supposed to be directly available along with its rates transition matrix. The FDI filter is designed as a bank of ℋ − /ℋ ∞ Luenberger observers, derived by optimizing frequency conditions that ensure guaranteed levels of disturbance rejection, fault sensitivity and are capable to discriminate anomalous events belonging to different fault classes. It is proved that, by resorting to stochastic stability concepts, the design method can be recast as a linear matrix inequality programming program in the observer bank gains. The resulting residual generator is a jump parameter‐dependent observer jointly exploiting the available measures on the deterministic plant parameter and on the instantaneous Markov chain realization. An FDI threshold logic is also proposed in order to reduce the generation of false alarms. The effectiveness of the design technique is illustrated via a numerical example. Copyright © 2011 John Wiley & Sons, Ltd.