Non-singular fixed-time fuzzy adaptive control for nonlinear systems subject to actuator faults

This paper proposes a non-singular fixed-time fault-tolerant adaptive tracking control method for a kind of multi-input and multi-output nonlinear system, which is in form of non-strict feedback and is subject to actuator faults. The major contribution, compared to other practical fixed-time fault-tolerant control methods, is that the fixed time can be calculated precisely. By applying fuzzy logic systems, the identification of unknown nonlinearities is achieved, and by the boundness of fuzzy basis functions, the algebraic loop problem is avoided. Based on the fixed-time stability theory, the practical fixed-time fault-tolerant adaptive tracking control method is proposed with adaptive back-stepping control technology, in which the control singular problem is overcome by applying the adding power integration method. By the Lyapunov function theory, the practical fixed-time stability of the closed-loop system is theoretically proved. And even in the case of unknown actuator faults, the tracking error of the controlled system for the given command signal can still converge to a small neighbourhood of zero within a fixed time, regardless of the system initial state. Finally, the proposed control method is successfully implemented on a multi-motor control platform, proving its effectiveness, and multiple comparative simulations are carried out, demonstrating its superiority.