基于Radau伪谱法的制导炸弹最优滑翔弹道研究

基于Radau伪谱法求解最优控制问题的原理，研究了滑翔型制导炸弹的最大射程优化问题。对制导炸弹动力学模型进行了无量纲化处理，结合极小值原理推导了最优控制轨迹的解析解和一阶必要性条件，采用Radau伪谱法将弹道优化问题转化为非线性规划问题，基于协态映射原理给出了数值解的最优性验证方法。仿真结果表明，Radau伪谱法能够提供具有工程应用价值的最优解，与常规的最大升阻比滑翔弹道相比，优化后的弹道射程增加10%以上。

Optimization of Glide Trajectory of Guided Bombs Using a Radau Pseudo-spectral Method

The problem of optimizing the maximum range of a glide guided bomb is studied based on the principle of solving optimal control problems using the Radau pseudo-spectral method. The dynamic model of the guided bomb is nondimensionalized. Combining with the Pontryagin minimum principle, the analytic solution of the optimal control and the first-order necessary condition are derived. The trajectory optimization problem is translated to a nonlinear programming via the Radau pseudo-spectral method. Based on covector mapping principle, an optimality verification method is presented for the numerical solution. Simulation results show that the Radau pseudo-spectral method can provide a highly valuable optimal solution for engineering application. Compared with the conventional maximum lift-to-drag ratio gliding trajectory, the trajectory after optimization can be extended by more than 10%.