基于伪谱法的欠驱动航天器实时最优控制算法设计

针对欠驱动刚性航天器提出了时间最优的闭环状态反馈控制算法。首先，利用直接Legendre 伪谱法规划出航天器开环的姿态机动轨迹，并验证了所得最优控制输入的可行性。然后，以航天器实际运行轨迹与开环轨迹间的偏差为变量构造偏差方程，并提出了基于间接Legendre 伪谱法的最优姿态稳定控制算法。最后，采用实时重规划策略实现了稳定控制器状态的反馈，从而完成了对参考轨迹的闭环跟踪。仿真结果表明所提算法运算量小，计算速度快，可以实时获取解析形式的控制输入修正量，而且对初始姿态存在扰动的情况具有一定的鲁棒性，运算精度较高。

Real-time optimal control for underactuated spacecraft using pseudospectral method

A novel time-optimal feedback control algorithm for closed-loop control of an underactuated rigid spacecraft is presented. First, the constrained trajectory is generated by direct Legendre pseudospectral method, and the feasibility of the control solutions is validated. Then, regarding the errors between the actual trajectory and the reference trajectory as variables, an error equation is constructed which can be solved by indirect Legendre pseudospectral method. Finally, the closed-loop trajectory tracking control law is obtained by on-line replanning strategy. Simulation results demonstrate that the proposed control scheme can obtain a closed-loop state feedback control law in real-time and can lead to a high precision even in the presence of initial state perturbations.