Observer-Based Finite-Time Adaptive Fault-Tolerant Control for Nonlinear System with Unknown Time-Varying Delay

In the fault-tolerant control tasks of nonlinear systems, unmeasurable states, time delay and actuator faults are considered to be the main factors hindering effective controller design and tracking performance improvement. To solve these problems, firstly, a state observer is established to estimate the unmeasurable of the system and the prescribed performance control based on error transformation is presented to maintain system efficiency and reliability. Secondly, the problem of controller design caused by input delay is effectively solved by constructing an auxiliary tracking error and auxiliary system and combining with the well-designed Lyapunov-Krasovskii functionals. Thirdly, the newly employed damping term in the intermediate control law is utilized to compensate for the possibly unlimited number of faults. Then, it is proved that all signals are semi-global practical finite-time stable based on the backstepping technique. Meanwhile, the tracking error can converge to a specified range within finite time. Finally, comparative simulations are presented to demonstrate the effectiveness of the proposed method.