中文摘要：

基于LGL（Legendre—Gauss—Lobatto）伪谱法，研究了临近空间助推一滑翔导弹再入段弹道快速优化问题。首先，基于改进的气动力模型建立了较为精确的再入数学模型；其次，针对该优化问题在气动数据处理和优化求解上存在的困难，基于LGL伪谱法系统地建立了再入最优飞行弹道的求解步骤，为解决直接利用LGL伪谱法存在的困难，设计了一种基于LGL伪谱法的串行优化求解策略；最后，分别采用积分推进法和协状态映射原理对优化结果进行了可行性和最优性验证。仿真结果表明，本文的弹道优化方法优化1条再入弹道所用时间为3～4s，计算效率较高，路径约束和端点约束均得到很好满足，算法求解精度较高，有效地实现了多约束多变量大型稀疏的再入弹道导弹快速优化。

英文摘要：

Rapid re-entry trajectory optimization of near space boost-glide missile was studied via the Legendre Gauss Lobatto （LGL） pseudospectral method. Firstly, an accurate mathematics model in re entry phase was established based on an improved aer odynamic model. Aiming at the difficulties of the optimization problem in processing of aerodynamic data as well as optimization sol- ving, the steps based on LGL pseudospectral method were listed systemically for solving the optimal re entry flight trajectory. Then a serial strategy based on LGL pseudospectral method was presented to deal with the difficulties in optimization using the LGL pseudospectral method directly. Finally, the feasibility and the optimality of optimal result were validated by integral propagation method and covector mapping principle, respectively. Simulation results show that computational time required for optimizing one re- entry trajectory is 3～4 s,and thus the computational efficiency is high. Path constrains and boundary constrains are well satisfied, and the precision of this trajectory optimization method is high. The rapid re-entry trajectory optimization with characteristics of mul- tiple constraints, multiple variables and large sparsity is achieved.