A generalized likelihood ratio test for a fault-tolerant control system

Willsky and Jones (1976) have developed the Generalized Likelihood Ratio (GLR) test for sequential jumps detection, isolation and estimation in discrete-time stochastic linear systems. After each detection and isolation of one jump, the treatment of another possible jump is obtained by a direct state estimate and covariance incrementation of the Kalman filter originally designed on the jump-free system. With this updating strategy, the rate of good decisions is not guaranteed to be maximized. To solve this problem, the proposed active GLR test will be based on a reference model updated on line after each detection and isolation of one jump. To reduce the computational requirement, the passive GLR test will be derived from a state estimator designed on a fixed reference model directly sensitive to system changes. We will show that the active and passive GLR tests can be easily integrated in a reconfigurable Fault-Tolerant Control System (FTCS) to asymptotically recover the nominal system performances of the jump-free system.