摘要
针对传统连续小推力转移优化方法中最优性难以保证、计算效率低、初值依赖性高等问题,本文提出一种基于哈密顿-雅可比-贝尔曼方程信息约束神经网络(Hamilton-Jacobi-Bellman equations informed Neural Network,HJB-INN)的求解框架.首先,对多种场景下航天器小推力转移进行最优控制问题建模,建立围绕仿射非线性系统的多约束优化问题模型;之后,推导终端约束与控制幅值约束下的哈密顿-雅可比-贝尔曼方程,基于值函数设计闭环最优控制律;为求解满足偏微分方程与边界条件的值函数,设计球坐标系下的函数连接理论(Theory of Functional Connections,TFC)与极限学习机(Extreme Learning Machine,ELM)融合的网络模型,并建立网格更新策略以提升总体精度.仿真结果表明,本文提出的方法能够得到多约束下的转移轨道,与经典物理信息约束神经网络模型相比求解精度更高,与直接法和间接法等传统方法相比在接近理论最优值下初值不敏感,可应用于航天器连续小推力转移轨道的优化设计.
In view of the problems of difficult optimality guarantee, low computational efficiency and high initial value dependencein traditional continuous low thrust transfer optimization methods, a solution framework based on Hamilton-JacobiBellman equations informed neural network (HJB-INN) is proposed in this paper. Firstly, the optimal control problem ofspacecraft low thrust transfer under various scenarios is modeled, and a multi-constraint optimization problem modelaround affine nonlinear system is established;then, the Hamilton-Jacobi-Bellman equations under terminal constraintsand control amplitude constraints are derived, and the closed-loop optimal control law is designed based on the valuefunction;in order to solve the value function that satisfies the partial differential equations and boundary conditions, anetwork model integrating the theory of functional connections (TFC) and the extreme learning machine (ELM) in thespherical coordinate system is designed, and a grid update strategy is established to improve the overall accuracy.Simulation results indicate that the proposed method is capable of determining transfer orbits under multiple constraints.When compared to classical physics-informed neural network, the proposed approach exhibits superior solution accuracy.Moreover, as it approaches the theoretical optimal value, this method demonstrates reduced sensitivity to initial valuesrelative to traditional direct and indirect methods. Consequently, this approach is well-suited for the optimization designof continuous low-thrust transfer orbits in spacecraft, offering a promising alternative for trajectory planning.
作者
王义宇
张泽旭
崔祜涛
徐田来
袁帅
包为民
李宸硕
罗宇航
WANG YiYu;ZHANG ZeXu;CUI HuTao;XU TianLai;YUAN Shuai;BAO WeiMin;LI ChenShuo;LUO YuHang(School of Astronautics,Harbin Institute of Technology,Harbin 150001,China;Science and Technology Commission of China Aerospace Science and Technology Corporation,Beijing 100048,China)
出处
《中国科学:物理学、力学、天文学》
北大核心
2025年第9期46-61,共16页
Scientia Sinica Physica,Mechanica & Astronomica
基金
国家自然科学基金(编号:U20B2001)资助项目。
