基于零控拦截的微分几何制导律

基于零控拦截打击的思想设计了一种新型微分几何制导律.论文首先介绍了微分几何相关知识，基于伏雷内(Frenet)坐标系分析了拦截器和目标的相对运动学关系，基于零控拦截的思想设计了一种新型微分几何制导律，并给出拦截器速度方向矢量变化的迭代计算方法.其次，结合圆形相关理论，利用李亚普诺夫稳定性定理对设计微分几何制导律的稳定性进行了详细证明推导.最后通过仿真表明，该制导律可有效拦截机动目标，相对于传统的比例导引律，设计的新型微分几何制导律制导精度高，拦截时间短，避免了末端过载快速增大的现象，降低了执行机构的要求.

Differential geometric guidance law based on zeroing effort intercept

A new differential geometirc guidance law is put forward based on the idea of zeroing effort intercept. Firstly, the relative theory of differential geometric is introduced, the relative dynamic model of the interceptor and target is analyzed in the Ferent coordinate, the new differential geometric law is derived based on the idea of zeroing effort intercept, also the algorithm of interceptor velocity vector movement is given. Secondly, the stability of the derived guidance law is proved by the Lyapunov stability theory using the rotundity theory. Thirdly, simulation results show that, the new derived guidance law could intercept the target effectively, compared with the conventional proportional guidance law, the proposed guidance law has high precision and shorter intercept time, also it overcomes the load divergence, so it cuts down the requirment of the actuator of the interceptor greatly.