Adaptive backstepping control for a class of uncertain systems with actuator delay and faults

Unknown actuator failures are inevitable in practical systems. At the same time, time delay exists in many physical actuators, and the system performance will be affected by such actuator delay and faults. However, the results of studies that attempt to compensate for unknown failures of actuators with time delay are still very limited. In this paper, such a problem is studied, and an adaptive control scheme is proposed based on backstepping approaches. First, the input delay of actuator faults and output disturbances are transformed into unknown effects on the output signal. In the backstepping recursive design, these unknown effects will accumulate to the last step of the controller design. Then, a new Lyapunov function is constructed by introducing auxiliary signals to prove the stability of the system. It is shown that the proposed control scheme can compensate for the effects caused by unknown actuator failures and input delays. The stability of the closed-loop system can be guaranteed by this adaptive controller. Finally, simulation studies are used to verify the effectiveness of the proposed scheme.