Multiple-Fault Detection and Isolation Based on Disturbance Attenuation Theory
In this dissertation, a linear estimator for fault detection and isolation called the Game Theoretic Multiple-Fault Detection Filter is derived for both continuous and discrete systems. The detection filter uses a disturbance attenuation formulation to bound the transmission of disturbances to the output, approximately blocking all but one fault from each of a set of projected residuals. However, different from previous approximate methods for single-fault detection filters, the multiple-fault detection filter utilizes a secondary optimization problem to generate a solution for the estimator gain that achieves more advanced detection filter goals. Specifically, the current work examines an optimization that increases sensitivity of each projected residual to its target fault. For the continuous case, it is proven that the new detection filter approximates previous detection filters obtained from geometric and spectral theories and extends them to finite time-varying systems. Further, the detection filter is demonstrated via numerical examples.