Robust convex optimization for reentry glide trajectory using polynomial chaos

基于混沌多项式的再入滑翔鲁棒轨迹凸优化

¹ Shaanxi Aerospace Flight Vehicle Design Key Laboratory, School of Astronautics, Northwestern Polytechnical University, Xi'an 710072, China
² Troops 96901 of PLA, Beijing 100094, China

Received: 13 September 2022

Abstract

Aiming at the reentry glide trajectory design of hypersonic vehicles with uncertain parameters, a robust trajectory optimization method is proposed to enhance the anti-interference ability and process reliability. Firstly, a robust trajectory optimization model for re-entry gliding under uncertain conditions is constructed, which is transformed into a deterministic trajectory optimization problem with dimension expansion by using an uncertainty propagation algorithm based on the Gaussian quadrature and non-intrusive polynomial chaos. Then, the convex optimization technology is used to convexity and discretize the problem, and a deterministic trajectory optimization strategy based on the sequential convex optimization algorithm is designed to achieve a fast solution for the high-dimensional deterministic problem. Finally, the hypersonic glide reentry of the American X-33 is chosen as an example for the numerical simulation. The results show that comparing with the traditional deterministic trajectory optimization algorithm, the present method can effectively reduce the impact of random interference on the reentry glide trajectory and improve the reliability and robustness of the trajectory.

摘要

针对参数不确定条件下高超声速飞行器再入滑翔轨迹设计问题, 研究了一种增强抗干扰能力和过程可靠性的鲁棒轨迹优化方法。构建不确定条件下再入滑翔鲁棒轨迹优化模型, 并设计了基于高斯求积与非嵌入式混沌多项式的不确定性量化传播算法, 从而将其转化为维数扩展的确定性轨迹优化问题; 利用凸优化技术对该问题进行凸化和离散, 设计了一种基于序列凸优化算法的轨迹优化求解策略, 以实现对该高维确定性问题的快速求解。以美国X-33的高超声速滑翔再入为例进行了仿真验证。结果表明, 与传统确定性轨迹优化算法相比, 所提方法能够有效降低随机干扰对再入滑翔轨迹的影响, 从而提升轨迹的可靠性与鲁棒性; 与现有典型鲁棒轨迹优化方法相比, 所提方法具有相当的精度和显著的计算效率优势。