To generate the midcourse guidance trajectory for intercepting the high-speed and high maneuvering target, which is a strongly nonlinear and strongly constrained problem, a two-stage convex optimization method is proposed to solve the optimal trajectory quickly. In the first stage, an initial trajectory generation method is proposed, by which the trajectory’s terminal state is close to the terminal position. And the generated trajectory is used as the initial solution of the convex optimization method. In the second stage, the original nonconvex optimization problem is transformed into a convex optimization problem by linearization and relaxation methods and then solved discretely. In the numerical simulation, the effectiveness of the proposed method is verified, and the robustness of the method is verified in different initial and terminal states. Then, several ablation experiments are operated to verify the advantage of the rapid initial trajectory generation method in the first stage. Finally, compared with the gauss pseudospectral method (GPM), the proposed method is proved to be efficient and has the potential of online trajectory generation.

中文翻译：

---

基于凸优化的中段制导快速轨迹生成方法

针对高速高机动目标截获中段制导轨迹是一个强非线性、强约束的问题，提出了一种两阶段凸优化方法来快速求解最优轨迹。在第一阶段，提出了一种初始轨迹生成方法，通过该方法，轨迹的终端状态接近终端位置。并将生成的轨迹作为凸优化方法的初始解。第二阶段，将原来的非凸优化问题通过线性化和松弛方法转化为凸优化问题，然后进行离散求解。在数值模拟中，验证了所提方法的有效性，验证了该方法在不同初始和终止状态下的鲁棒性。然后，进行了多次消融实验，验证了第一阶段快速初始轨迹生成方法的优势。最后，与高斯伪谱方法（GPM）相比，该方法被证明是有效的，并且具有在线轨迹生成的潜力。