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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.
In order to solve the re-entry trajectory optimization problem of hypersonic gliding aircraft with uncertainties, a novel method based on generalized orthogonal polynomials is proposed to solve the stochastic trajectory optimization problem. Based on the generalized orthogonal polynomial method, Sampling, forming a sampling space, and then each sample into the deterministic trajectory optimization problem repeated iterative solution, the observed sample space, and calculate its expectations, variance and covariance, the estimated output value to the maximum vertical Cheng as a cost function to simulate the optimal trajectory of hypersonic gliding aircraft with random disturbance.The simulation results show that the stochastic trajectory optimization method based on generalized orthogonal polynomials can effectively deal with the impact of random disturbance on trajectory optimization problems, Carlo method greatly improves computational efficiency.