应用非线性规划求解异面最优轨道转移问题

研究了一种应用非线性规化求解有限推力作用下异面最优轨道转移问题的方法。采用改进春分点根素形式的高斯行星方程，从庞德里亚金极小值原理出发，将有限推力作用下异面最优轨道转移问题转化为两点边值问题；在考虑边界条件、横截条件及开关函数的前提下，将两点边值问题转化为针对协状态初值等的参数优化问题；最后应用非线性规划方法求解形成的参数优化问题。本方法特点是能得到开关函数从而得到最优发动机开关机逻辑。文章最后通过一个仿真计算，演示了完整的求解过程，验证了方法的有效性。

Applying Nonlinear Programming to Solve Nonplanar Optimal Orbital Transfer Problem

A method of applying nonlinear program to solve nonplanar optimal orbital transfer under finite thrust is studied. Adopting modified equinoctial elements as the state variables and based on Pontrygon miniumum principle, the nonplanar optimal orbital transfer problem results in a two-point boundary value problem. Considering bound condition, transversality condition and switch function, the resulted two-point boundary value problem then is converted into parameters optimization problem aiming at the initial values of costates which is solved by nonlinear programming. The advantage is that one can get optimal switch sequence from the switch function. At the end of this paper, a numerical example is prensented to demonstrate this method.