Trajectory optimization is important in achieving long-range atmospheric entry hypersonic vehicles. However, the trajectory optimization problem for atmospheric entry of hypersonic vehicles is characterized by strong nonlinearity, parameter uncertainties and multiple constraints. This study proposes a novel online trajectory optimization method for hypersonic vehicles based on convex programming and a feedforward neural network. A sequential second-order cone programming (SOCP) method is obtained to describe the trajectory optimization problem after the Gauss pseudo-spectral discretization. Subsequently, multiple optimal trajectories under aerodynamic uncertainties are generated offline and classified as the training and validation datasets. Then, a multilayer feedforward neural network is trained using these datasets and to output the optimal control command online. This method yields approximately 95% shorter computation time compared with the offline SOCP method. Considering the existence of the aerodynamic uncertainties, three terminal states calculated by this method are all smaller than 4.1%. In conclusion, the proposed trajectory optimization method can provide a high-precision, robust entry trajectory for hypersonic vehicles efficiently.

轨迹优化对于实现远程大气进入高超音速飞行器非常重要。然而，高超声速飞行器进入大气层的轨迹优化问题具有强非线性、参数不确定性和多约束等特点。本研究提出了一种基于凸规划和前馈神经网络的高超声速飞行器在线轨迹优化新方法。获得了序列二阶锥规划（SOCP）方法来描述高斯伪谱离散化后的轨迹优化问题。随后，离线生成空气动力学不确定性下的多个最优轨迹，并将其分类为训练和验证数据集。然后，使用这些数据集训练多层前馈神经网络，并在线输出最优控制命令。与离线 SOCP 方法相比，该方法的计算时间缩短了约 95%。考虑到气动不确定性的存在，该方法计算的三个终端状态均小于4.1%。总之，所提出的轨迹优化方法可以有效地为高超声速飞行器提供高精度、鲁棒的进入轨迹。