基于二阶变分的中制导最优弹道修正

Midcourse guidance optimal trajectory modification using the second variation

针对反临近空间高超声速目标拦截作战过程中的中制导弹道的规划与修正问题,设计了一种最优弹道修正算法。首先分析了在中制导阶段进行弹道规划与弹道修正的必要性,基于庞特里亚金最小值原理给出了基准最优弹道满足的一阶必要性条件,其次将一阶必要性条件进行二阶变分,得到控制量的修正量,利用基准弹道数据,通过逆向积分,将协态变量的偏差量表示为终端约束修正量以及状态变量偏差量的表达式,从而有效解决了协态变量偏差量的获取问题,最后进行了多种情形下的数字仿真,对所提算法进行验证并与高斯伪谱法(Gauss pseudospectral method,GPM)进行对比。结果表明,该方法不仅具有较高的求解精度,并且其求解效率远高于GPM,有利于弹上在线实现。

Aiming at the problem of the midcourse trajectory generation and modification in the interceptton against hypersonic targets in near space, a novel optimal traiectory modification algorithm is designed. Firstly, the demand for trajectory generation and trajectory modification in the midcourse phase is analyzed. The first or- der necessary conditions for the nominal optimal trajectory are given based on the Pontryagin minimization theo- ry. Secondly, the first order necessary conditions are further differentiated to second variation to acquire the control modifications. The difficulty of the co-states deviations acquisition is solved by reversely integrating u- sing the nominal trajectory information to get the expression with the terminal constraints modifications and the current states derivations. Finally, digital simulations under different scenarios are carried out to testify the ef- fectiveness of the proposed algorithm and the results are compared with those given by the Gauss pseudospeetral method （GPM）. Simulations results show that the algorithm has the merits of high precision and efficiency than the GPM, which is preferable for the online realization.