Backstepping Control for Systems with Fast Time-Varying Reference Signals—An Autonomous Landing Application

A nonlinear backstepping control framework is developed for autonomous landing of a quadrotor on a wave-excited marine platform. This study addresses the underactuated nature of the aerial vehicle and the strong coupling between translational and rotational dynamics, ensuring stable trajectory tracking under sea-induced disturbances. Reference trajectories are generated through physically grounded Pierson–Moskowitz (PM) and modified Pierson–Moskowitz (MPM) wave spectra, enabling realistic modeling of vertical heave motion, while horizontal position and yaw are defined through harmonic components adapted to the sea-state regime. The controller is designed through a seven-step recursive backstepping procedure, with Lyapunov functions guaranteeing asymptotic stability of the tracking errors for the regulated outputs. A modular MATLAB simulation platform is implemented, integrating the full six-DOF quadrotor dynamics, the control algorithm, and spectral reference generation. Numerical simulations demonstrate that the Lyapunov function derivatives remain negative over the entire simulation horizon, confirming asymptotic convergence. Comparative results with a tuned PID (proportional integral derivative) controller indicate superior tracking performance and damping and reduced amplitude and phase errors for the backstepping approach, especially under MPM-based trajectories representing rough sea states. The proposed framework establishes a reliable basis for adaptive extensions and future hardware-in-the-loop validation of autonomous landing on moving marine platforms.