A game theoretic fault detection filter

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Abstract
The fault detection process is approximated with a disturbance attenuation problem. The solution to this problem, for both linear time-varying and time-invariant systems, leads to a game theoretic filter which bounds the transmission of all exogenous signals except the fault to be detected. In the limit, when the disturbance attenuation bound is brought to zero, a complete transmission block is achieved by embedding the nuisance inputs into an unobservable, invariant subspace. Since this is the same invariant subspace structure seen in some types of detection filters, we can claim that the asymptotic game filter is itself a detection filter. One can also make use of this subspace structure to reduce the order of the limiting game theoretic filter by factoring this invariant subspace out of the state space. The resulting lower dimensional filter will then be sensitive only to the failure to be detected. A pair of examples given at the end of the paper demonstrate the effectiveness of the filter for time-invariant and time-varying problems in both full-order and reduced-order forms.

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