Implementation of Failure-Detection Systems with Adaptive Observers

The design problem of adaptive observers for failure-detection purposes, applied to linear, constant and possibly variable parameters, multi-input, multi-output systems is considered here. It is shown that, in order to keep the observer´s (or Kalman filter) false-alarm rate (FAR) under a certain specified value, it is necessary to have an acceptable proper matching between the observer, (or KF) model and the system parameters. An adaptive observer algorithm is introduced here in order to maintain the desired system-observer model matching, despite initial mismatching and/or system parameter variations. Only a properly designed adaptive observer is able to detect abrupt changes in the system (actuator, sensor failures, etc.) with adequate reliability and FAR. Conditions for convergence for the adaptive and tracking process are obtained, leading to a simple adaptive law (algorithm) with the possibility of an a priori choice of fixed adaptive gains. Simulation results show good tracking performance with small observer output errors and accurate and fast parameter identification, in both deterministic and stochastic cases, leading to small FAR.