基于拟勒让德谱变换的防空导弹弹道优化

Midcourse Trajectory Optimization Design for a Surface-to-Air Missile Based on Legendre Pseudospectral Method

为了使防空导弹更高效地拦截目标,要求导弹在中制导段到末制导段的交班点上具有最优的性能.针对不同的性能指标构建了相应的最优控制模型,扩展了拟勒让德谱变换法,使其能有效地将已建的含有间断点的模型转换成非线性规划(NLP)问题,采用序列二次规化(SQP)算法优化得到最优解.分析了不同指标下最优弹道之间各参数的差异,选择终端速度最大作为目标函数再次优化,得到了终端速度在交班点上的分布规律.优化结果表明,转化成NLP问题的模型具有较高的精度,且易于优化求解;导弹终端速度在弹道倾角和偏航角等于零的附近达到最大值.

To intercept coming targets and to achieve the maximum kill probability, it is necessary to ensure the surface-to-air missile optimal performance at the handover point between the midcourse trajectory and the terminal phase. Several optimal control models were established for the different performance index. The Legendre pseudospectral method was developed to convert the systems containing gap points to nonlinear program （NLP） problems effectively, and the optimal results were obtained by SQP method. Then the objective function of maximum velocity was selected based on the response comparison between the optimal trajectories, and the velocity performance law at the handover point was calculated. The simulation results indicate that the model which is trasformed into the NLP problems takes a high optimization precision and fast convergence speed, and the missile velocity at the handover point reaches the maximum value when the pitch and yaw angle are about zero.