小推力轨道机动最优控制研究

Optimum Control for Low-Thrust Orbit Maneuver

研究航天器在小推力的作用下,椭圆轨道最优转移的一种解析解法.在牛顿中心力场中,采用地心惯性坐标系,选用合适的轨道根数,忽略其它摄动的影响,建立航天器转移的状态方程.应用Pontryagin极大值原理建立航天器最优推力加速度的控制方程,对方程进行合理的简化,只考虑它们的一次项,忽略其它的高次项,从状态方程中得出小推力对轨道根数产生的摄动影响,然后分别对它们进行积分,从而得到最优转移轨道的解析解.

The analytic solution of optimum low-thrust power transfer between arbitrary elliptical orbits using con- tinuous constant acceleration is presented, based on the orbital elements selected. First, the spacecraft transfer equations of state are established in Newton central force field using the center of earth inertial coordinate system after neglecting other perturbations influence. Then through optimum thrust force acceleration governing equation obtained by Pontryagin maximum principle and the reasonable simplification, the optimum low thrust under the orbit elements is obtained. Finally, the optimum transfer orbit analytic solution is obtained by integrating the equations.