考虑随机干扰的高超声速滑翔飞行器轨迹优化

为解决高超声速滑翔式飞行器具有干扰不确定性的再入轨迹优化问题，提出了一种基于广义正交多项式方法的随机轨迹优化数值求解方法。针对随机干扰，基于广义正交多项式方式对其分布进行采样，形成采样空间，而后将每个采样值代入确定性轨迹优化问题中进行反复迭代求解，得出观测值的样本空间，并计算其期望、方差和协方差，估计输出值。以最大纵程为代价函数对具有随机干扰的高超声速滑翔式飞行器最优轨迹进行了数字仿真。仿真结果表明，基于广义正交多项式的随机轨迹优化方法能够有效处理随机干扰对轨迹优化问题的影响，与蒙特卡洛法相比计算效率大大提高。

Trajectory optimization for hypersonic gliding vehicle considering stochastic disturbance

To solve the problem of the reentry trajectory optimization for the hypersonic gliding vehicle with stochastic disturbance, the numerical method of trajectory optimization based on the generalized polynomial chaos was put forward. The sampling space was formed by the sampling of stochastic variable using generalized polynomial chaos. The space of the observations came into being after putting every sampling value into solving the problem of the deterministic trajectory optimization iteratively. The expected value, variance and covariance were computed and the outputs were approximated. The simulation of maximizing the downrange angle of the reentry trajectory optimization for the hypersonic gliding vehicle with stochastic disturbance was carried out based on this method. The results of the simulation indicate that the method could solve the problem of trajectory optimization with stochastic disturbance, and the computational efficiency was improved greatly contrasted with the Monte Carlo method.