全电推进卫星轨道优化的推力同伦解法

All-electric propulsion satellite trajectory optimization by homotopic approach

全电推进卫星的入轨过程是一个典型的多圈小推力轨道优化问题,由于其推力器加速度小,变轨圈数多,造成其最优理论解的求解较困难。为解决该问题,利用最优控制理论建立了全电推进卫星变轨优化的间接法模型,将变轨优化问题转化为协态变量初值猜测的两点边值问题。从大推力问题开始,通过遗传算法获得大范围猜测值并结合系列二次规划方法获得大推力的精确解。采用推力同伦思想,使用逐渐缩小推力的方式完成小推力问题的求解。仿真算例表明,采用推力同伦的方法,通过数十次的推力缩减即可有效解决多达上百圈变轨的静止轨道全电推进卫星入轨优化问题。

The orbit injection of all-electric propulsion satellite is a typical low thrust multi-revolution orbit optimal problem. Due to the small acceleration and the large number of revolutions, it is difficult to solve the optimal theoretical solution. In order to solve this problem, the indirect method model of all-electric propulsion satellite orbit optimization was established by using the optimal control theory, and the problem of the orbital optimization was transformed into the two-point boundary value problem which can be solved by guessing the initial costate variable. A large thrust problem was solved by combining the evolutionary algorithm and the sequential quadratic programming. With the help of homotopic approach, the small thrust problem was solved by gradually reducing the thrust. The simulation shows that the thrust homotopic method can effectively solve the trajectory optimal of geostationary all-electric propulsion satellites with up to hundreds of revolutions by dozens of thrust reductions.