利用动态规划原理实现多冲量最优交会问题

多冲量最优交会问题是航天领域非常重要的一个研究方向,从运筹学角度将此问题转化为一个多阶段多维动态规划问题,并着重对多阶段二维动态规划进行分析研究。在给出状态方程及指标函数递推公式的基础上,得到了两冲量和三冲量交会问题最优解的求解算法,之后分别通过实例验证了算法的有效性。对于以地心角等参数为决策变量的更高维问题,讨论了利用进化算法等降维方法实现多维动态规划的思想。

Solving the Optimal Multi-impulse Rendezvous Problem Based on the Dynamic Programming

The multi-impulse rendezvous problem is a key research field of astronautics.Firstly,based on the operational research,this problem was converted to a multi-phase-multi-dimension dynamic programming question.Then the multi-phase-two-dimension dynamic programming problem was emphatically analyzed,and the state transfer equations and recursion equations of the performance function were deduced.The solution to the two-impulse and three-impulse problem and the validating examples were given later.ln the end,the dynamic programming idea which uses the evolution algorithm to reduce the dimension of the multi-dimension question was introduced.