Optimal fault diagnosis based on duality principle for linear systems

The note studies the fault diagnosis problem in the optimal meaning for linear systems when the actuator faults and the sensor faults happen. An optimal fault diagnosis approach is proposed based on duality principle. This scheme first translates the fault states into the states of an augmented system. Based on duality principle, the design problem of the observer for fault diagnosis is translated into the state feedback design problem of the duality system of the observation error equation. Then the design of the optimal fault diagnoser is translated into the design of the equivalent optimal state feedback control of error system. By constructing the reduced-order fault diagnoser, the real-time fault diagnosis is realized on-line, and the quadratic performance index is catered. Simulation example demonstrates the feasibility and validity of the proposed scheme.