Adaptive fault-tolerant control of uncertain systems with unknown actuator failures and input delay

Unknown failures and time delays of actuators which may degrade system performance seem inevitable in practical systems. However, the available results to compensate for unknown failures of time delay actuators based on adaptive approaches are very limited. In this paper, we address such a problem by considering controlling a class of second-order systems with unknown actuator failures and input delays. Firstly, the controlled system is transformed into a triangular structure model. Meanwhile, the input time delay is transformed into dynamics of the output signal. Then, an adaptive controller is developed using backstepping. Not only can the uncertainties due to actuator failure be compensated, but the unknown input delay has also been effectively restrained under the proposed control scheme. The upper bound condition of strength scalar <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>μ</mml:mi> </mml:mrow> </mml:math> is proposed. It is a sufficient condition for system stability. When the strength scalar satisfies this condition, the design parameters exist and the system is stable under the controlling of the proposed controller. Finally, the effectiveness of the proposed control scheme is verified through simulation results, including numerical simulation and actual system simulation. Through the comparative simulation, it can be seen that the control scheme proposed in this paper has faster convergence speed.