针对系统存在不确定性且不确定性边界信息无法提前获知条件下多旋翼无人机的姿态控制问题,提出自适应有限时间控制(Adaptive finite-time control,AFTC)算法。先将该问题抽象为当存在匹配未知不确定性时,一般二阶单输入单输出(Single-input Single-output,SISO)系统的跟踪控制问题;在此基础上,设计了齐次非线性终端滑模面;针对不确定性边界信息在实际设计中往往无法提前获取,提出了基于判断系统是否到达滑动模态的自适应算法,用以动态改变控制增益;对所给出的AFTC算法,用李雅普诺夫方法严格证明了跟踪误差可在有限时间内收敛到原点;进一步用AFTC算法设计了小型四旋翼无人机姿态控制器,并通过数值仿真和分析对该算法的有效性加以验证,从仿真结果可看出:AFTC算法可使多旋翼无人机控制系统在无法提前获知不确定性边界信息条件下,实现快速、高精度的姿态跟踪控制,且所产生的控制信号连续,易于工程实现。

To address the attitude control problem of multirotor drones under conditions of system uncertainty where the boundary information of uncertainty cannot be known in advance, an Adaptive Finite-Time Control (AFTC) algorithm is proposed. This problem is first abstracted as a tracking control issue for a general second-order Single-Input Single-Output (SISO) system in the presence of matched unknown uncertainties. Based on this, a homogeneous nonlinear terminal sliding surface is designed. Given that uncertainty boundary information is often not available in practical design, an adaptive algorithm is proposed to dynamically change the control gain based on determining whether the system has reached the sliding mode. For the proposed AFTC algorithm, it is rigorously proven using the Lyapunov method that the tracking error can converge to the origin in finite time. Furthermore, the AFTC algorithm is used to design an attitude controller for a small quadrotor, and its effectiveness is validated through numerical simulation and analysis. The simulation results demonstrate that the AFTC algorithm enables the multirotor drone control system to achieve rapid and high-precision attitude tracking control under conditions where the uncertainty boundary information cannot be known in advance, with continuous control signals that are easy to implement in engineering.