有限推力下时间最优轨道转移

研究了一种有限推力作用下的时间最优轨道转移计算方法。以非奇异根素形式的高斯行星摄动方程为基础,由庞德里亚金极小值原理导出正则方程组,通过将最优控制问题转化为协状态初值为待优化参数的参数优化问题,并通过非线性规划求解得到的参数优化问题,从而避开求解两点边值问题的困难。文章最后给出2个算例,分别计算了零倾角零偏心率最优轨道转移和大倾角改变最优轨道转移。计算过程及结果表明本文所用方法对协状态初值猜测敏感性小,收敛迅速;零倾角零偏心率情况下无奇异;所得控制轨线光滑。

Time-optimal Orbital Transfer under Finite Thrust

A finite-thrust tsajectory optimization method using modified equinoctial elements and nonlinear programming is investigated.Based on the dynamics with the modified equinoctial elements as state variables,optimality condition is derivated and the optimizing problem is converted into parameter optimization in order to avoid the difficult two point boundary value problem.The parameter optimization is solved by nonlinear programming.Numerical example of optimal transfer with zero inclination and zero eccentricity and numerical example of large inclination change optimal transfer are analyzed.The results show that a larger convergence region exists comparing with that of the two point boundary value problem,and no singularity occurs when inclination and eccentricity are zero and the control steering is smooth.