Fault diagnosis and dynamic optimal fault-tolerant control for systems with double time-delays
双时滞系统的故障诊断和动态最优容错控制

Fault diagnosis and optimal fault-tolerant control are studied for linear systems with time-delays in both control vector and state vector, when unmeasured actuator faults and sensor faults occur in the systems. Based on the linear transformation of time-delay systems, the optimal fault-tolerant control law for the faulty system is designed by utilizing Riccati matrix equation and Sylvester equation, and the existence and uniqueness of the optimal fault-tolerant control law is proved. The real-time and on-line fault diagnosis and the observation of system states are realized by constructing a new reduced-order state observer for the augmented system with faults, and the physically unrealizable problem is solved. Finally, the physically realizable dynamic optimal fault-tolerant control law is obtained by utilizing the results of fault diagnosis. Simulation example has demonstrated the feasibility and validity of the proposed fault diagnosis scheme and the dynamic optimal fault-tolerant control scheme.