Adaptive prescribed-time trajectory tracking control for UVMS based on error transformation and adaptive prescribed-time filter

In this paper, a new prescribed-time adaptive controller is proposed to further improve the response characteristics and robustness of underwater vehicle-manipulator systems (UVMS). First, an error transformation function with asymmetric time-varying constraints is designed, and a feasibility proof is given to ensure that the output of the system satisfies the constraints. Second, to solve the “complexity explosion” problem caused by the backstepping method, an adaptive prescribed-time filter is constructed to make the filtering error converge at a prescribed time. Third, to address the unknown nonlinear function, a simpler prescribed-time disturbance observer is proposed to estimate the external disturbances and model uncertainties to ensure that the disturbance estimation errors converge to a small set near the origin at a prescribed time. Then, the closed-loop system is proven to be prescribed-time stable via Lyapunov stability theory, and the states do not exceed the constraints. Finally, the proposed algorithm is shown to be effective through numerical simulations.