Command-filter-based trajectory-tracking control of quadrotor subject to internal and external disturbances

We propose a command-filter backstepping controller that integrates a disturbance observer and a high-gain observer (HGO) to handle unknown internal and external disturbances acting on a quadrotor. To build the controller, we first define tracking errors between the measured and desired quadrotor outputs, which allow the system to be rewritten in a new set of state variables. Using this transformed model, we apply Lyapunov theory to derive a backstepping control law. To avoid repeated differentiation of states and virtual controls, a first-order command filter is introduced, and a nonlinear disturbance observer is added to provide disturbance estimates. Each state in the controller and observer is replaced with its estimate from the HGO. The resulting control law enables the quadrotor to follow its path despite internal and external disturbances, with each subsystem allowed its own disturbance type for realism. A new state transformation and Lyapunov-based derivation prevent the usual explosion of complexity, while the HGO reconstructs unmeasured states and their rates for output feedback. The nonlinear disturbance observer attenuates constant and nonlinear disturbances as well as band-limited white noise. The method reduces dependence on high-precision sensors and mitigates wind, model error, and rotor noise effects during flight. Unlike previous studies that treat either disturbance rejection or partial sensing, this work combines the command filter, disturbance observer, and HGO to address both challenges simultaneously while avoiding the complexity growth typical of backstepping designs.