Fast fixed-time formation control for heterogeneous high-speed aircraft with input saturation compensation

A hierarchical fast fixed-time formation-control scheme is proposed for high-speed aircraft with heterogeneous aerodynamic effectiveness under angle-of-attack (AoA) saturation. To address the coupled challenges of rapid convergence, heterogeneous aerodynamic effectiveness, and strict input constraints, a hierarchical control framework is developed, consisting of a virtual formation controller, a tracking differentiator (TD)-assisted actual controller with dynamic gain adaptation, and an auxiliary saturation compensator. Lyapunov analysis establishes an initial-condition-independent fixed-time convergence bound for the nominal unsaturated design, with the switched-exponent structure providing the common fast mechanism. Under AoA saturation, the auxiliary compensation design guarantees bounded fixed-time convergence of the saturation-related tracking errors, yielding practical fixed-time-like formation convergence of the full closed-loop system. Numerical simulations further verify formation achievement under different geometries, demonstrate faster transient response than the compared fixed-time and finite-time baselines, show smoother exit from saturation with reduced peak transient deviations, and show reduced post-saturation oscillation for less capable aircraft through dynamic gain adaptation.