Finite-time fractional-order fault-tolerant neural-network adaptive control for fractional-order strict-feedback nonlinear systems subject to input saturation

This paper presents a finite-time fault-tolerant neural-network adaptive controller designed for strict-feedback fractional-order nonlinear systems subject to actuator failures, input saturation, immeasurable states, and external perturbations. Unlike most existing adaptive-control methods for fractional-order systems, which heavily rely on complex backstepping schemes, our proposed algorithm transforms the original system into an affine Brunovsky form. This transformation enables a direct and straightforward controller design, voiding the intricacies of recursive backstepping. The algorithm addresses four types of unknown actuator faults: bias, drift, and loss of accuracy (as additive faults), as well as loss of effectiveness (as a multiplicative fault). An observer estimates the unmeasured virtual states, while a pair of neural networks approximates the uncertain nonlinearities and compensates for actuator saturation. The proposed approach ensures robust tracking performance and bounded signals in the closed-loop system, even in the presence of actuator faults. Stability analysis shows that the tracking error converges to a bounded set near the origin in finite time. Finally, simulation results validate the effectiveness and accuracy of the proposed technique.