运载火箭在完成发射任务后的回收及再利用，能够显著降低发射成本。动力着陆段制导与控制算法作为火箭回收的关键技术之一，在任务中扮演着重要的角色。受到地球大气层进入段复杂动力学的作用，动力着陆段的初始状态通常无法准确预估，火箭需要在线地根据实时的飞行状态进行最优飞行轨迹的规划。同时，受着陆过程中环境的不确定扰动和制导、导航与控制系统的执行误差等影响，制导算法必须具备较强的鲁棒性。针对上述需求，本论文围绕制导算法的实时性、最优性和鲁棒性，展开火箭回收动力着陆段实时最优控制算法的研究。首先，针对火箭回收动力着陆段燃料最优控制问题，本论文采用序列凸化和无损凸化方法，将原最优控制问题转化为序列凸优化问题。在此基础上，根据问题的特征结构，将序列凸优化问题整理为标准的二阶锥优化问题，并采用原始对偶内点法对问题进行定制，使动力着陆段燃料最优控制问题具备实时在线求解的条件，从而建立了基于定制化序列凸优化算法的实时最优制导方法。其次，本论文采用最优控制理论，分析了火箭回收动力着陆问题燃料最优解的一般形式，得出在推力指向受约束的前提下最优推力曲线最多包含两次幅值切换的结论。在该结论的基础上，本论文提出了自适应分段伪谱凸优化算法。该算法能够根据燃料最优解的推力分段特性，自适应地给出相应的最优解，在不影响算法实时性和收敛性的前提下，进一步提高了算法的精度。之后，本论文在凸优化实时最优控制算法研究的基础上，将开环最优控制问题与闭环状态反馈结合，同时考虑姿态跟踪的反馈控制，提出了火箭回收动力着陆段最优反馈制导与控制算法。该算法结合环境的不确定扰动、系统误差、采样周期等因素，对最优反馈制导与控制算法的精度进行了分析，并结合仿真算例系统地分析了算法的实时性、最优性和鲁棒性。最后，本论文以火箭回收的初始状态可行性判据和基于数据的实时最优控制方法为例，探讨了深度学习方法在动力着陆段实时最优控制算法中的应用。论文提出的基于深度学习的状态可行性判据，能够实时地对火箭回收动力着陆段的临界可行状态进行准确预估，且能够对初始状态的可行域进行分析。同时，基于深度学习智能控制方法，在满足实时性的同时，具备出色的最优性和鲁棒性。

The recovery and reuse of the launch vehicle after the launch mission can significantly reduce launch costs. As one of the key technologies of powered landing guidance and control, real-time optimal control algorithm plays an important role in the mission. The powered landing mission of reusable rocket requires the guidance algorithm to be able to control the vehicle in real time to achieve the precise soft landing to the target in an optimal way, and the algorithm is required to have an excellent performance on the adaptability and robustness. From this perspective, this thesis focuses on the real-time performace, optimality and robustness of the guidance algorithm, and carries out the research on the real-time optimal guidance and control algorithm for powered landing of reusable rocket. First of all, for the fuel-optimal control problem of rocket landing, this thesis adopts successive concexifacation and lossless concexifacation techniques to deal with the non-convexities in the original optimal control problem, and proposes the sequential convex optimization method. Furthermore, the primal-dual interior point method is adopted to solve the sequential convex optimization problem in a customized manner, and a real-time optimal guidance method based on a customized sequential convex optimization algorithm is established. Secondly, this thesis adopts the optimal control theory to analyze the general form of the fuel-optimal solution for the powered landing problem, and draws the conclusion that the optimal thrust curve contains at most two magnitude switching under the constraint of thrust pointing. On this basis, this thesis proposes an adaptive multi-phase pseudospectral convex optimization algorithm. The proposed algorithm can adaptively give the corresponding optimal solution in real time according to the thrust segmentation form of the fuel-optimal solution, which further improves the accuracy, optimality and adaptability of the algorithm. After that, based on the research of convex optimization algorithms, this thesis combines the open-loop guidance algorithms with the closed-loop control and state feedback, and proposes an optimal feedback guidance and control algorithm for powered landing. The algorithm considers the model disturbances and system errors those are ignored in the research of the guidance algorithms to analyze the accuracy of the optimal feedback guidance and control algorithm. On the basis of this algorithm framework, the thesis further proposes an attitude tracking feedback control method, which extends the optimal feedback guidance and control algorithm for powered landing to the full six-degree-of-freedom model, and systematically analyzes the real-time performance, optimality, and robustness of the algorithm in combination with simulation examples. Finally, this thesis takes the initial feasiable conditions of powered landing and the data-based real-time optimal control method as examples to discuss the application of deep learning methods in the real-time optimal control algorithm for powered landing of reusable rocket. The initial feasiable criterion based on deep learning proposed in the thesis can predict the critical feasiable conditions of powered landing in real time and analyze the feasiable region of the initial conditions. At the same time, the deep-learning-based intelligent controller has an excellent performace on the optimality and algorithm robustness, while satisfiese the requirement of real-time performance as well.