Fixed-time adaptive fuzzy fault-tolerant tracking control for a class of uncertain nonlinear time-delay systems

This paper proposes an adaptive fuzzy fixed-time fault-tolerant control method for strict-feedback nonlinear systems with unknown time-varying delays. First, the finite covering lemma and fuzzy logic systems are employed to mitigate the impact of time-varying delays, which eliminates the need for the traditional Lyapunov-Krasovskii functional approach and thereby relaxes the constraints on the derivative of unknown time-varying delays. Additionally, Butterworth-filtered signals are adopted to address the systems' non-affine nonlinear faults. The proposed method effectively integrates the backstepping technique with fixed-time stability criteria, ensuring the boundedness of all closed-loop signals and driving tracking errors to a negligible neighbourhood of zero within a fixed time. Notably, the convergence time depends exclusively on the design parameters. The validity of the theoretical results is demonstrated through two numerical simulations.