Tracking Design of an Uncertain Autonomous Underwater Vehicle with Input Saturations by Adaptive Regression Matrix-Based Fixed-Time Control

In this study, a simplified model of an autonomous underwater vehicle (AUV) with input saturation based on kinematic and dynamic equations was built. Subsequently, a simplified model of the AUV was used to represent its main dynamic features. In terms of trajectory tracking, only the system’s structure (i.e., the regression matrix, which is flexible and non-unique) from the nominal model of the transformed system was required to design the proposed adaptive regression matrix-based fixed-time controller (ARM-FTC). A nonlinear auxiliary sliding surface was contained in the control design to shape the system’s frequency response. When the operating point was in the neighborhood of the zero auxiliary sliding surface, nonlinear filtering gains were increased to accelerate its tracking ability. Furthermore, the skew-symmetric property condition of the time-derivative of the inertia matrix and the Coriolis and centrifugal force matrices was not necessitated for the controller design. Under an appropriate condition for lumped uncertainties, the fixed-time convergence of the auxiliary sliding surface and the corresponding tracking error is guaranteed to go to zero by the Lyapunov stability theory. Finally, a comparative study was conducted through simulations for the AUV with external disturbance and input saturation among the known parameters, learning parameters reflecting a regression matrix, and another asymptotical robust tracking control scheme. The results validate the fast tracking ability of a desired time-varying trajectory of the proposed control scheme.