基于混合法的月球软着陆轨迹优化

利用混合法思想和人工免疫算法研究了月球软着陆轨迹优化问题.首先建立月球软着陆系统模型并进行归一化处理；然后基于混合法思想利用庞特亚金（Pontryagin）极大值原理推导最优控制律，以伴随变量初值和终端时刻作为优化变量，将终端约束作为罚函数引入评价函数中，将月球软着陆轨迹优化问题转化为非线性规划问题（NLP，Nonlinear Programming）；最后应用引导人工免疫算法（GAIA，Guiding Artificial Immune Algorithm）求解该优化问题.仿真结果表明，GAIA混合算法比直接法的寻优速度快，终端误差小，且可搜索到理论最优轨迹；同时，GAIA混合算法的伴随变量初值收敛范围比间接法大，降低了最优月球软着陆轨迹的搜索难度.

Optimization of lunar soft landing trajectory based on hybrid method

The lunar soft landing trajectory was optimized by hybrid method and artificial immune algorithm (AIA). Firstly, the system model of lunar soft landing trajectory was established and normalized. Secondly, the optimization problem of lunar soft landing trajectory was converted into a nonlinear programming (NLP) via hybrid method, in which optimal control law was derived by Pontryagin's maximum principle, the initial values of adjoint variables and terminal time were variables to be optimized, and terminal constraints were introduced into evaluation function as penalty terms. Finally, a guiding artificial immune algorithm (GAIA) was applied to solve this optimization problem. Simulation results show that the GAIA hybrid method has faster optimization speed and higher optimization precision than direct method, and can obtain the theoretical optimal trajectory. Meanwhile, GAIA hybrid method has larger convergence range of initial value of adjoint variables than indirect method, and reduces the difficulty of searching optimal lunar soft landing trajectory.