Saturated Adaptive Fuzzy Fixed-Time Nonsingular Integral Terminal Sliding-Mode Control of AUVs

This article investigates the trajectory tracking control issue of autonomous underwater vehicles (AUVs) subject to dynamic uncertainties, external disturbances, and input amplitude and rate saturations. Initially, two new stable systems with fixed-time convergence are developed, and their upper bounds of settling time and convergence regions are thoroughly analyzed. Building on these systems, an enhanced fast nonsingular integral terminal sliding-mode (NITSM) surface and a new virtual control law are designed, respectively. Next, a novel saturated adaptive fuzzy fixed-time NITSM controller is proposed, circumventing the restrictions on uncertainties and input saturation in the existing results. The proposed controller ensures that the tracking error converges to a small neighborhood of the origin within a fixed time. Furthermore, to facilitate the adaptive fixed-time stability analysis, two new inequalities are established and rigorously proved. Using the two inequalities, the fixed-time stability of closed-loop systems is demonstrated by the Lyapunov's theory. Finally, representative numerical simulations validate the effectiveness of the proposed control scheme.