Keeping the flying formation of spacecraft is a key problem which needs to be solved in deep space exploration missions. In this paper, the nonlinear dynamic model of formation flying is established and a series of transformations are carried out on this model equation. By using SDRE (State-Dependent Riccati Equation) algorithm, the optimal control of flying formation is realized. Compared with the traditional control method based on the average orbit elements and LQR (Linear Quadratic Regulator) control method, the SDRE control method has higher control precision and is more suitable for the advantages of continuous control in practical engineering. Finally, the parameter values of the sun-earth libration point L2 are substituted in the equation and simulation is performed. The simulation curves of SDRE controller are compared with LQR controller. The results show that the SDRE controllers time cost is less than the LQR controllers and the former’s fuel consumption is less than the latter’s in the system transition process.

中文翻译：

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日地连接点SDRE保持飞行编队控制方法研究

保持航天器的飞行编队是关键任务，在深空探测任务中需要解决。本文建立了编队飞行的非线性动力学模型，并对该模型方程进行了一系列的变换。通过使用SDRE（状态相关Riccati方程）算法，可以实现对飞行编队的最佳控制。与传统的基于平均轨道要素的控制方法和LQR（线性二次调节器）控制方法相比，SDRE控制方法具有更高的控制精度，更适合于在实际工程中进行连续控制的优点。最后，将日地释放点L2的参数值代入方程式并进行仿真。将SDRE控制器的仿真曲线与LQR控制器进行了比较。