The asymptotic game theoretic multiple-fault detection filter

In this paper, the game theoretic multiple-fault detection filter (GTMFDF) is examined as faults are blocked completely from certain residuals. In the prequel, it was shown that the GTMFDF approximates detection filters based on spectral and geometric theories with a set of disturbance attenuation problems by placing faults into approximate detection spaces, and extends these detection filters to time-varying systems. In the current work, the GTFDF is evaluated in the limit as the disturbance attenuation bound goes to zero. The resulting time-varying Riccati equations each obtains a nullspace equal to the detection space of its complementary fault. Thus, by combining the Riccati solutions over the set of target faults, the structure of the spectral and geometric theory-based detection filters is recovered and extended to the time-varying case. Then, in order to implement the asymptotic GTMFDF, a reduced-order detection filter is obtained by truncating directions obtained from the Riccati solutions.