小推力最优轨迹协态估计的高效机器学习方法

针对变比冲小推力轨迹间接优化中的协态变量初值猜测问题，提出了一种基于机器学习的协态变量初值高精度高效估计方法。首先，基于标称最优轨迹延拓，建立了状态量边值高扰动上限情形下的数据集生成方法，并分析了扰动上限对求解效率的影响。然后，构建了基于位置速度、轨道根数和改进春分点轨道根数多形式状态量组合输入的人工神经网络(ANN)映射关系，分析并优化了神经网络结构。将提出的方法应用于深空探测小推力转移场景，仿真结果表明该方法相对于标称轨迹直接扰动的数据集生成方法及单一形式状态量输入的人工神经网络映射方法，均有效地提升了求解收敛率，能够高效高精度地估计协态变量初值，实现轨迹快速优化。

Efficient Machine Learning Method for Co state Estimation of Low thrust Optimal Trajectories

For initial values of co state variables guessing problem in the indirect optimization of the low thrust trajectory with variable specific impulse, a method based on machine learning is proposed to estimate the initial values of co state variables with high accuracy and efficiency. Firstly, based on the continuation of the nominal optimal trajectory, a data set generation method under the condition of high perturbation upper limit of the state variable boundary value is established and the influence of the upper limit of the perturbation on solving efficiency is analyzed. Then, an artificial neural network (ANN) mapping relationship based on the combined inputs of position, velocity, the orbital elements and the modified equinoctial elements is constructed. The neural network structure is analyzed and optimized. The proposed method is applied to the scenarios of low thrust transfers in deep space exploration. Simulation results indicate that the method effectively improves the solution convergence rate compared with the data set generation method with direct perturbation of nominal trajectory and the artificial neural network mapping method with a single form of states input, and it can efficiently and accurately estimate the initial values of co state variables to achieve fast trajectory optimization.