电动力绳系卫星的推力幅值较小且方向固定,完成轨道机动任务的周期长,其最优控制问题的求解比较困难。采用在傅里叶空间描述的轨道动力学模型,将控制量电流表示为傅里叶级数的形式,并推导了用傅里叶系数作为参量的椭圆轨道运动的平均轨道根数方程。在此基础上构造了电动力绳系卫星轨道机动的最优控制模型,通过直接配置法将其转化为非线性规划问题,使用序列二次规划法进行了数值求解。固定圈数内最大提升轨道高度和最短时间变轨两个算例表明,该方法可以快速精确地求解椭圆轨道内电动力绳系卫星的最优控制问题。

Electrodynamic tethered satellites with low thrust-to-weight ratios can only perform orbital transfers over a large number of revolutions, which poses a real challenge to short time scale optimal control. An approach to multi-revolution, large-time-scale optimal control of electrodynamic tethered satellites is investigated in this paper using an orbital averaging technique based on Fourier series expansion. The control profile is transformed in Fourier space and the secular dynamics equations in arbitrary elliptic orbits are represented as functions of thrust Fourier coefficients. With direct collocation, the optimal control problem based on Fourier series expansion is converted to a parameter optimization problem that can be solved by sequence quadratic planning. This method can determine the optimal control solutions accurately and reduce the computational requirements significantly. Numerical examples of maximum climb transfer and minimum time orbit change are presented to demonstrate the validity of the proposed approach.