摘要
针对空间探测中连续小推力轨迹优化,总结了间接法在最优控制理论、初值估计和同伦延拓方法等方面的研究进展.首先介绍了连续小推力轨迹优化问题的建模及其相应的最优控制问题的状态方程、约束方程和性能指标,对比了两类主要优化方法,即直接法和间接法的求解思路与优缺点.随后总结了轨迹优化初步设计、间接法初值估计以及同伦延拓方面的研究进展,探讨了智能优化和深度学习在轨迹优化间接法中的应用,进一步结合当前大规模任务规划、实时最优控制等需求讨论了间接法的应用.最后,对连续小推力轨迹优化间接法的发展展望进行了总结.
Abstract
The indirect method for low-thrust trajectory optimization is focused on,and the related research progress in the optimal control theory,initial guesses,and homotopy continuation method is summarized.Firstly,the continuous low-thrust trajectory optimization problem is established as the optimal control problem,where several types of state equations,constraints,and performance indices are introduced.The solution algorithms,advantages,and disadvantages of the two main optimization methods,direct method and indirect method,are compared.The indirect method can obtain the optimal control law by theoretical analysis,possess the high-accuracy orbit propagation,and guarantee the first-order optimality of solutions.However,the solution algorithm needs to be reconstructed and may be very complex for different kinds of constraints.The algorithm is generally very sensitive to the initial guesses,where the costate variables are difficult to guess due to a lack of physical interpretation.Then,the research progress in the preliminary design of low-thrust trajectories,initial guesses,and homotopy continuation is summarized,and the improvements led by the intelligent optimization and deep learning are presented.The indirect method has been improved in terms of the solution efficiency,optimality,and convergence.Furthermore,the applications of the indirect method are discussed in combination with the requirements of the global optimization for the mission design and the real-time optimal control in spacecraft guidance control.Finally,the possible development of the indirect method is prospected.
基金项目
国家自然科学基金(12302058)
国家自然科学基金(U21B2050)
青年人才托举工程(2023QNRC001)
上海市青年科技英才扬帆计划(21YF1446100)
NETL
NSTL
万方数据