高级检索
武迪, 程林, 王伟, 李俊峰. 基于切换系统的小推力轨迹优化协态初始化方法[J]. 深空探测学报(中英文), 2021, 8(5): 528-533. DOI: 10.15982/j.issn.2096-9287.2021.20200090
引用本文: 武迪, 程林, 王伟, 李俊峰. 基于切换系统的小推力轨迹优化协态初始化方法[J]. 深空探测学报(中英文), 2021, 8(5): 528-533. DOI: 10.15982/j.issn.2096-9287.2021.20200090
WU Di, CHENG Lin, WANG Wei, LI Junfeng. Analytical Initialization for Low-thrust Trajectory Optimization Based on Switching System[J]. Journal of Deep Space Exploration, 2021, 8(5): 528-533. DOI: 10.15982/j.issn.2096-9287.2021.20200090
Citation: WU Di, CHENG Lin, WANG Wei, LI Junfeng. Analytical Initialization for Low-thrust Trajectory Optimization Based on Switching System[J]. Journal of Deep Space Exploration, 2021, 8(5): 528-533. DOI: 10.15982/j.issn.2096-9287.2021.20200090

基于切换系统的小推力轨迹优化协态初始化方法

Analytical Initialization for Low-thrust Trajectory Optimization Based on Switching System

  • 摘要: 传统同伦方法通常将小推力燃料最优问题转化为能量最优问题求解,以增加间接法求解的收敛率,但求解能量最优问题仍需要猜测协态初值以初始化求解算法。该研究针对小推力燃料最优问题,将其优化模型嵌入到切换系统,从而将该问题转化为具有解析协态初值的优化问题进行求解,进一步提高了求解的收敛率,并能够以解析协态初值初始化求解算法。首先,将切换系统优化模型与小推力优化模型相结合,常规的切换系统的切换函数是由最优控制得出的,而本研究则采用了人为设计给定的切换函数,实现了不同系统之间的切换和联系;其次,基于标称轨道线性化的方法,给出了具有解析协态初值的目标系统的设计,无需复杂标称轨道即可实现协态初始化;最后,数值仿真验证了该方法的有效性,相比于传统同伦方法具有更高的求解效率。

     

    Abstract: The traditional homotopy method usually transforms the low-thrust fuel-optimal control problem into the energy-optimal problem to increase the convergence rate of the indirect method. However, it is still necessary to guess the initial values of the co-states to initialize the solving algorithm. In this paper, the optimization model of the fuel-optimal problem is embedded in the switching system with the analytical initial co-states, which further improves the convergence rate with the analytical initialization. Firstly, the switching system is introduced with the embedded fuel-optimal problem. The switching function of the conventional switching system is derived from the optimal control, but in this paper, the given switching function is designed artificially to realize the switching and continuation among different systems. Secondly, based on the linearization technique, the target system is designed with analytical initial co-states, initializing the solving algorithm by a simple nominal trajectory. Finally, the numerical simulation verifies the effectiveness of the proposed method, which is more efficient than the traditional homotopy method.

     

/

返回文章
返回