Fixed-Time Prescribed-Performance Control of UAV–USV Formations with Composite-Disturbance Rejection and Collision Avoidance

Heterogeneous unmanned aerial vehicle–unmanned surface vehicle (UAV–USV) formations must reject disturbances while maintaining prescribed tracking performance and responding to collision risks. This study develops a mathematically consistent framework for one UAV leading three CyberShip II USVs. A unified adaptive observer uses a radial basis function network to approximate the disturbance derivative while explicitly retaining approximation and reconstruction residuals. A regularized double-signed-power sliding surface removes the zero-point singularity of its fractional-power derivative, and compact UAV and stacked-USV control laws preserve the prescribed-performance transformation. External-obstacle and pairwise artificial potential fields are embedded as planar coupled inputs. A composite Lyapunov analysis retains observer, sliding, transformed-error, topology, and potential-field coupling terms and gives a conditional regional practical fixed-time entrance bound under explicit gain and bounded-input conditions; it does not assert exact convergence, collision-free invariance, or satisfaction of these conditions by the numerical gains. In the retained original 350 s comparison, the proposed UAV integral absolute error (IAE) in the x-direction was 1.1217, compared with 3.7739 for the reference control. These traceability data are unchanged and do not constitute a newly rerun matched-baseline assessment of the corrected controller, a continuous-time safety proof, or physical validation.