中文摘要：

基于Legendre-Gauss-Lobatto（LGL）伪谱法（PSM）求解最优控制问题的原理,研究了有限推力轨迹快速优化设计以及计算节点和效率改善策略。对远程变轨动力学模型进行了无量纲化处理,并设计了初值生成和串行优化求解策略,用来提高多变量多约束大规模稀疏非线性规划问题的收敛性。结合极小值原理推导了问题的最优性必要条件,基于协态映射原理设计了数值解的最优性验证方法。利用二阶微分方程技术消去部分状态量,建立了节点和计算效率改进模型,并讨论了该策略的相关数值处理技术。仿真结果表明,本文的算法可以快速地提供应用于实际飞行任务的最优解,节点改善策略在保证计算精度的同时,有效降低了计算收敛时间。

英文摘要：

Rapid finite-thrust trajectory optimization using the Legendre-Gauss-Lobatto （LGL） pseudospectral method （PSM） combined with a grid node and computational efficiency refinement strategy is studied. The principles of LGL PSM are given to solve optimal control problems. The nondimensional long-range orbit maneuver dynamics model and a serial optimization approach including initial value creator are proposed to improve convergence of the large-scale sparse nonlinear programming problem with variables and constraints. The necessary optimality conditions are derived from Pontryagin Minimum Principle. The Verification algorithm of optimality is designed based on the Costate Mapping Principle. Taking advantage of the second-order differential equation to reduce the length of the state parameters, the grid node and computational efficiency refinement method is proposed. Some numerical issues are discussed later. Simulation results indicate that the algorithm can rapidly provide excellent solution for practical mission. In addition, high accuracy and rapid convergence are demonstrated for the grid node refinement algorithm.