Disturbance-Resilient UAV Formation Control for Low-Altitude Economy: Elliptical Configuration Tracking via a Generalized Predefined-Time Approach

This paper investigates an improved predefined-time control law for cooperative unmanned aerial vehicles (UAVs) formation tracking under the condition of wind disturbances. Firstly, we propose a generalized predefined-time Lyapunov theorem incorporating a persistent positive bounded term for predefined-time synchronization of target tracking systems. This theorem ensures that the upper bound of the settling time in terms of system dynamics can be explicitly specified, freeing it from dependence on initial conditions and controller parameters. Secondly, to empower UAVs with the capability of rapidly stabilizing on a prescribed trajectory within a designated time while maintaining elliptical formation patterns, we devise a chattering-free predefined-time elliptical formation tracking protocol. Subsequently, we resort to the consensus error of adjacent arc length, which facilitates the avoidance of frequent acceleration and deceleration of UAVs inherent in elliptical formation schemes with an equal separation phase. Furthermore, we develop a predefined-time unknown state estimator (PUSE) to precisely compensate for wind-induced perturbations. We analyze the convergence of the closed-loop system and demonstrate that it is predefined-time stable. Simulation results demonstrate that the proposed method yields at least a 52% enhancement in tracking performance and a 24% reduction in energy consumption compared to benchmark methods.