This paper proposes an improved back-stepping control approach and its application to small nonlinear UAV control systems with uncertainties such as external disturbance. Unlike traditional back-stepping control methods, the idea of prescribed performance function (PPF) is incorporated into the control design, such that both the transient and steady-state control performance can be strictly guaranteed. Moreover, we design a novel tracking differentiator to avoid the "differential expansion" problem well caused by the calculation of derivative. Significantly, the function approximators (e.g. neural networks) that are widely used to address the unknown nonlinearities in the nonlinear control designs are not needed. Finally, the numerical simulation verifies the convergence and robustness of the system, and the results show that the control strategy can obtain better transient and steady-state performance.

This paper focuses on the safe navigation of quadrotor unmanned aerial vehicles (UAVs) under obstacle-related safety constraints and prescribed tracking performance within a user-assigned predefined time. A novel control strategy is developed by integrating a Barrier Lyapunov Function (BLF) with an error-shifting transformation into the translational control mechanism, ensuring the vehicle stays clear of a safety sphere constructed around potential obstacles while being guided to a target position. This approach effectively handles arbitrary initial conditions and maintains safe operation within predefined bounds. Furthermore, by combining a prescribed-performance mechanism with a time-varying performance function and the backstepping technique, the proposed method allows the designer to specify in advance the performance-bound attainment time $T_0$ and the terminal tracking-error bound $s_{T_0}$. For the analyzed translational closed-loop subsystem, all signals are bounded, and the tracking error is theoretically shown to enter the set $|e_{1j}|<s_{T_0}$ no later than $T_0$. With the designed controller, all signals in the analyzed translational closed-loop subsystem are bounded, and the output tracking error is theoretically shown to enter a user-defined prescribed set no later than the performance-bound attainment time $T_0$. Simulation studies demonstrate the effectiveness of the designed controller in achieving desired performance metrics.