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Detection signal design for failure detection: A robust approach. (English) Zbl 0988.93078

Consider the behaviours of the normal and failed modes of a system modelled by two different discrete-time LTI models subject to bounded energy perturbations. The detection signal (DS) is an input signal enhancing the detectability of failure. The two models are assumed to satisfy the standard assumptions for Kalman filtering, signal energy boundedness of model and measurement uncertainties, and that no system transition occurs between both models during the test period. The problem is an off-line construction of minimum energy DSs to separate these two models based on I/O measurements. A method for constructing an optimal solution over a finite horizon is given. The asymptotic properties of a DS as the horizon goes to infinity are studied. An optimal DS converges to pure sinusoids in this case. The notion of a separability index is introduced as the ratio of the bound on the uncertainty signal norm over the optimal DS norm. A method for its computation including the corresponding DS is given. An on-line implementation of the failure decision filter is briefly discussed.

MSC:

93E10 Estimation and detection in stochastic control theory
93E11 Filtering in stochastic control theory
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