基于区间样条小波的太阳帆轨迹优化算法

针对太阳帆轨迹优化问题，提出了一种基于区间样条小波的新颖数值算法。首先推导了太阳帆航天器的轨道动力学方程并提出了优化目标函数，然后提出了基于区间样条小波函数及其导数算法的最优控制直接数值法。该优化算法的核心是基于区间样条小波函数及其导数算法，在小波配点上将状态与控制变量作离散化处理，进而可利用小波函数有效逼近带有突变的优点，提高了求解以小波系数为参数的非线性规划问题的计算精度和效率。对典型的地球－水星之间的太阳帆轨道优化问题的仿真结果表明，基于小波的数值解法优于半解析法。

Solar Sail Trajectory Optimization Algorithm Based on Spline Wavelet

A novel numerical approach to trajectory optimal problem of solar sailing is proposed based on the interval spine wavelet function. The dynamics model of solar sailing is derived, and the optimized objective function is developed. The optimization algorithm based on interval spline wavelet function and its derivative is briefly introduced. The heart of our approach is to expanding the state and control variables by cubic spline wavelet function decomposition, thus the wavelet advantageous properties of compact representation would inherently make it to capture the discontinuities efficiently and accurately by using a standard nonlinear programming problem solver. The novel approach is demonstrated by a typical actual Mercury rendezvous, the optimal results show that our approach outperforms the pseudo-method in efficiency and accuracy.