Abstract The optimal design of orbit raising trajectories is formulated within a multi-objective hybrid optimal control framework. The spacecraft can be equipped with chemical, electric or combined chemical-electric propulsion systems. The model incorporates realistic effects of the space environment and complex operational constraints. An automated solution strategy, based on two sequential steps, is proposed for this problem. In the first step, operational constraints are not enforced and the control law of the electric engine is parameterized by a Lyapunov function. A heuristic global search algorithm selects the propulsion system and optimizes the guidance law. Approximate Pareto-optimal solutions are obtained trading off propellant mass, time of flight and solar-cell degradation. In the second step, candidate solutions are deemed as initial guesses to solve the nonlinear programming problem resulting from direct transcription of the operationally constrained problem. The proposed approach is applied to two transfer scenarios to the geostationary orbit. Results show the effectiveness of the methodology to generate not only rapid performance estimates for preliminary trade studies, but also accurate calculations for the detailed design. Additionally, it is identified that the application of operational restrictions causes minor penalties in the objective function.

中文翻译：

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具有操作约束的混合多目标升轨优化

摘要 在多目标混合最优控制框架内制定了升轨轨迹的优化设计。该航天器可以配备化学、电力或化学-电力联合推进系统。该模型结合了空间环境和复杂操作约束的现实影响。针对这个问题提出了一种基于两个连续步骤的自动化解决方案策略。第一步，不强制执行操作约束，电动发动机的控制律由李雅普诺夫函数参数化。启发式全局搜索算法选择推进系统并优化制导律。通过权衡推进剂质量、飞行时间和太阳能电池退化，获得近似帕累托最优解。第二步，候选解被视为初始猜测，以解决由操作约束问题的直接转录产生的非线性规划问题。所提出的方法适用于到地球静止轨道的两种转移方案。结果表明，该方法不仅可以为初步贸易研究生成快速性能估计，而且可以为详细设计进行准确计算。此外，还确定应用操作限制会导致目标函数中的轻微惩罚。结果表明，该方法不仅可以为初步贸易研究生成快速性能估计，还可以为详细设计进行准确计算。此外，还确定应用操作限制会导致目标函数中的轻微惩罚。结果表明，该方法不仅可以为初步贸易研究生成快速性能估计，还可以为详细设计进行准确计算。此外，还确定应用操作限制会导致目标函数中的轻微惩罚。