SE(3)上航天器姿轨耦合固定时间容错控制

针对相对运动航天器姿轨一体化控制问题，考虑执行器故障和控制输入饱和的影响，提出了一种基于滑模的模糊自适应固定时间容错控制方法。首先，在李群SE（3）的框架下建立并推导相对运动航天器姿轨一体化误差动力学模型；其次，引入执行器故障和控制输入饱和的问题，采用双幂次快速终端滑模面，并结合模糊自适应方法设计了固定时间稳定的容错控制器，可以实现执行器故障情况下相对运动航天器的高精度快速跟踪控制；然后，运用Lyapunov方法证明了系统的稳定性，该控制器不仅能不依赖于系统的初始状态实现滑模趋近和到达阶段的固定时间稳定性，而且由于采用模糊逼近方法结合自适应更新策略可以实时高精度地估计系统的总扰动信息，因此可以达到快速高精度的容错控制目标；最后，对所提出的的控制方法进行数值仿真分析，结果验证了该方法的有效性和可行性。

Fixed-time fault-tolerant control for coupled spacecraft on SE(3)

To solve the difficulty of integrated control of the relative motion spacecraft's attitude and orbit, and considering the effect of actuator fault and control input saturation, a fuzzy adaptive fixed-time fault-tolerant control method based on sliding mode is proposed. Firstly, a dynamic model of the integrated attitude and position error of the relative motion spacecraft is established and derived under the framework of Lie group SE(3). Next, considering the actuator fault and control input saturation, a fault tolerant controller with fixed time stability is designed by adopting double-power fast terminal sliding mode surface and combining with fuzzy adaptive method, which can realize high precision and fast tracking control of relative motion spacecraft under actuator fault. Then, the Lyapunov method is used to prove the stability of the system. The controller can not only realize the fixed-time stability of sliding mode approach and arrival stage independent of the initial state of the system, but also because the fuzzy approximation method combined with the adaptive update strategy can estimate the total disturbance information of the system with high accuracy in real time, so It can achieve the goal of fast and high-precision fault-tolerant control. Finally, the proposed control method is analyzed by numerical simulation, and the results verify the effectiveness and feasibility of the method.