两级固体上升器是大型火星样本回收计划中的重要组成部分，针对固体火星上升器在样品返回任务中的最优动力设计与耗尽关机多约束制导问题开展研究，提出了一种解析-数值融合的入轨段优化方法，最优解析方法为固体动力的优化设计提供理论依据，数值优化方法在理论最优解邻近进一步解决实际飞行中面临的耗尽关机制导问题。首先，为了分析与优化固体上升器最大载荷质量下的动力参数，基于庞特里亚金极大值原理构建了推力矢量方向的最优控制问题，推导出最优动力参数的新的必要条件来消去协态乘子矢量，进而获得了最优控制量的解析表达式。然后，针对上升器在实际飞行条件下面临的参数偏差及不确定性干扰，提出了一种融合最优解析解序列的二次型数值优化方法，该方法通过高效反向递归敏感度矩阵在线快速迭代计算出飞行指令，控制火星上升器在耗尽关机方式下高精度进入预定目标轨道。最后，推力矢量方向的最优解析表达式，通过与GPOPS优化方法的对比与分析，验证了在必要条件下的最优性与正确性，并给出了火星上升器的最优动力方案。数值仿真结果表明：在配置的参数偏差及不确定性干扰下，火星上升器采用所提的解析-数值融合优化方法，能够在耗尽关机方式下实现高精度入轨任务，具有一定的理论意义和工程应用价值。

The two-stage solid ascent vehicle is an important part of the large-scale Mars sample recovery program. To address the problems of the optimal thrust design and the depleted shutdown guidance with multi-constraints for solid Mars ascent vehicles in sample return missions， an analytical-numerical fusion method for optimization of the orbit entry phase is proposed， in which the analytical optimization method provides the theoretical basis for the optimal design of the solid thrust， and the numerical optimization method further solves the problem of depleted shutdown guidance faced in the actual flight in the proximity of the theoretically optimal solution. Firstly， to analyze and optimize the thrust parameters of the solid ascent vehicles under the maximum load mass， the problem of optimal control of the thrust direction is constructed based on the Pontryagin maximum principle. A new necessary condition of the optimal thrust parameters is derived to eliminate the costate multiplier vector， so that the analytical expression of the optimal control commands is obtained. Secondly， considering the parameter deviation and uncertainty interference of the ascent vehicles under actual flight conditions， a quadratic numerical optimization method combining the optimal analytical solution sequence is proposed to guide the Mars ascent vehicle to the predetermined target orbit with high accuracy in the depleted shutdown mode， which can quickly calculate the flight commands online by the efficient inverse recursive sensitivity matrix. Finally， a comparison with the GPOPS optimization method verifies the optimality and correctness of the proposed analytical expression. The optimal thrust scheme of Mars ascent vehicles is also given. The numerical simulation results demonstrate that the Mars ascent vehicle can enter the target orbit with high accuracy in the depleted shutdown mode with the interference of deviation and uncertainties by the proposed method.