Adaptive finite‐time control for a class of uncertain high‐order non‐linear systems based on fuzzy approximation

The problem of adaptive practical finite‐time control is considered for a class of single‐input and single‐output non‐linear systems, in which the system non‐linear functions are assumed to be unknown. By combining adaptive fuzzy control approach with the backstepping technology, a backstepping‐based adaptive fuzzy finite‐time control scheme is proposed. In the control design procedure, fuzzy logic systems are employed to identify the non‐linear uncertainties. The stability analysis of the adaptive closed‐loop systems is proposed based on the finite‐time Lyapunov stability theory. The proposed adaptive fuzzy controller guarantees that all the closed signals are semi‐global practical finite‐time stability while the tracking error converges to a small neighbourhood of the origin. Finally, simulation results are presented to validate the effectiveness of our results.