Optimization of low-thrust many-revolution transfers and Lyapunov-based guidance
Optimization of low-thrust many-revolution transfers and Lyapunov-based guidance
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DOI：
10.1016/j.actaastro.2009.05.013
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发表时间：
2010
影响因子：
3.5
通讯作者：
Yang Gao;Xinfeng Li
中科院分区：
文献类型：
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作者：
Yang Gao;Xinfeng Li
基于平均分点轨道元素的动态演化，我们开发了一种优化低推力多转轨道转移的直接方法，并提出了一种基于李雅普诺夫的制导方法，其中采用了具有时变增益的李雅普诺夫控制律。在每次转移公转过程中，以变分计算的最优控制形式制定了参数化控制律，并提出了近点和远点中心燃烧结构，以有效解决节省燃料的轨道转移问题。每次传输旋转内控制控制律和燃烧结构的参数通过有限数量的离散节点进行插值。将最优轨道转移问题转化为非线性规划求解的参数优化问题。随后，揭示了参数化控制律和李雅普诺夫控制律之间的映射，根据该映射，可以使用轨迹优化解获得李雅普诺夫控制律的时变增益，称为李雅普诺夫增益。然而，这种映射并不能保证所有获得的李雅普诺夫增益都是正的，因此基于李雅普诺夫的指导在整个转移期间可能不是严格稳定的。尽管如此，我们表明，基于李雅普诺夫的制导并不严格稳定，但仍然可以在某些轨道转移情况下成功引导航天器。负李雅普诺夫增益可以重新定义为适当的正值，以保证基于李雅普诺夫的指导的稳定性和可接受的性能。
Based on the dynamic evolution of mean equinoctial orbital elements, we developed a direct method to optimize low-thrust many-revolution orbit transfers and proposed a Lyapunov-based guidance, in which a Lyapunov control law with time-varying gains is employed. Within each transfer revolution, a parameterized control law, in the form of the optimal control derived from the calculus of variations, is formulated, and a periapsis- and apoapsis-centered burn structure is proposed in order to effectively solve fuel-saving orbit transfers. The parameters governing the control law and the burn structure within each transfer revolution are interpolated through a finite number of discrete nodes. The optimal orbit transfer problem is converted to the parameter optimization problem that is solved by nonlinear programming. Subsequently, a mapping between the parameterized control law and the Lyapunov control law is revealed, in terms of which the time-varying gains of the Lyapunov control law, called Lyapunov gains, can be obtained using trajectory optimization solutions. However, this mapping does not guarantee that all obtained Lyapunov gains are positive so that the Lyapunov-based guidance may not be strictly stable during an entire transfer period. Nevertheless, we showed that the Lyapunov-based guidance that is not strictly stable may still successfully guide the spacecraft for certain orbit transfer cases. Negative Lyapunov gains can be re-defined as appropriate positive values to warrant both stability and acceptable performance for the Lyapunov-based guidance.