Global Fixed-Time Target Enclosing Tracking Control for an Unmanned Surface Vehicle Under Unknown Velocity States and Actuator Saturation

This paper presents a global fixed-time control framework to address the target circumnavigation tracking problem of underactuated unmanned surface vehicles (USV) under unknown velocity states, lumped uncertainties, and actuator saturation. At the core of this approach is a novel fixed-time target-enclosing line-of-sight (FTTELOS) guidance law, designed to generate the desired heading angle and surge velocity. To estimate unknown velocities, external disturbances, and unmeasured system states, a set of fixed-time observers is constructed, consisting of a velocity observer, a disturbance observer, and a high-dimensional extended state observer (HFTESO). Moreover, to enhance robustness and effectively tackle actuator saturation, the control scheme incorporates a fixed-time sliding mode controller, a dynamic auxiliary system, and a fixed-threshold event-triggered mechanism. Simulation results using SimuNPS demonstrate that the proposed method enables rapid and smooth target circumnavigation, with all system errors converging to an arbitrarily small neighborhood of the origin within a fixed time. Theoretical analysis and simulation studies confirm the effectiveness and robustness of both the FTTELOS guidance law and the integrated control strategy. Quantitatively, compared with the traditional target-enclosing line-of-sight (TELOS) method, the proposed FTTELOS reduces the convergence time of the distance error δe from 13.64 s to 10.22 s and the angular error ϕe from 10.46 s to 7.52 s, demonstrating a significant improvement in convergence speed and overall control performance.