<p>The majority of existing finite-time prescribed performance control methods require the upper bounds of uncertainties and disturbances to be known, as well as strict restrictions on the initial state of the system. This work proposes an adaptive finite-time prescribed performance control strategy for quadcopter unmanned aerial vehicles (QUAVs) in the presence of asymmetric input saturation, unmodeled dynamics and unknown disturbances. In order to constrain tracking errors, a novel time-varying constraining function is introduced, which allows both the settling time and the tracking accuracy to be explicitly specified in advance, irrespective of initial conditions and any design parameter. In contrast to asymptotically stable saturated systems with unknown disturbances, an adaptive control law, a new integral sliding surface and barrier function are integrated into the controller to achieve finite-time convergence of QUAVs, while explicitly considering input saturation and uncertainty. Furthermore, the proposed method does not necessitate the upper bound information of the disturbance, which is typically required in conventional sliding mode control. Subsequently, the finite-time convergence of all signals in the closed-loop QUAVs system is guaranteed via Lyapunov methodology. Finally, numerical simulations and experiments are conducted to demonstrate the efficacy, resilience and practicality of the proposed controller.</p>