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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.
The idea of hybrid method and artificial immune algorithm are used to study the lunar soft landing trajectory optimization problem. Firstly, a lunar soft landing system model is established and normalized. Then, based on the Pontryagin maximum principle, The optimal control law, with the initial value of the variable and the terminal moment as the optimization variables, introduces the terminal constraint as a penalty function into the evaluation function and transforms the lunar soft landing trajectory optimization problem into Nonlinear Programming (NLP). Finally, GAIA (GAIA, Guiding Artificial Immune Algorithm) to solve this optimization problem.The simulation results show that the GAIA hybrid algorithm is faster than the direct method, the terminal error is small, and can search the theoretical optimal trajectory; at the same time, GAIA hybrid algorithm The initial value of the adjoint variable converges more than the indirect method, which reduces the search difficulty of the optimal lunar soft landing trajectory.