Closed-Loop Active Fault Diagnosis for Stochastic Linear Systems

The ability to reliably distinguish between multiple fault hypotheses is generally strongly dependent on the input applied to the system. This paper presents a computationally efficient method for closed-loop active fault diagnosis (AFD) for stochastic linear systems with uncertain initial conditions and multiple fault models. The proposed AFD method relies on computing an open-loop optimal input sequence that is applied in a receding-horizon fashion by solving the input design problem online based on the most recent system measurements. The AFD problem is formulated to maximize a statistical distance measure of the model predictions subject to system constraints. We present a fast algorithm for solving the AFD problem to global optimality, with computational complexity that is independent of the number of models and the number of states in each model. The performance of the closed-loop AFD method is demonstrated on a benchmark fault diagnosis problem.

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