Geometric optimal control and applications to aerospace
Geometric optimal control and applications to aerospace
复制标题
几何最优控制及其在航空航天中的应用
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
M. Cerf
中科院分区：
文献类型：
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作者：
Jiamin Zhu;E. Trélat;M. Cerf
本文讨论了对航空航天问题的最佳控制应用，重点是现代几何最佳控制工具和数值延续技术。几何最佳控制是一种理论，将最佳控制与各种差异几何概念相结合。最终目标是为控制系统的一般类别提供最佳的合成结果。持续或同义方法包括解决一系列参数化问题，从简单的问题开始，从最终与初始问题的连续变形开始。他们有助于克服射击方法的困难初始化问题。几何控制和同质方法的组合改进了最佳控制理论的传统技术。最佳态度的非学术示例（经典和机载）发射车（经过详细处理）的最佳态度 - 设备控制手段，说明了如何使用几何学最佳控制极端的结构。这种理论分析有助于建立有效的数值解决方案程序，结合了射击方法和数值延续。还分析了chat不休，并显示了如何在实践中处理这个问题。
This article deals with applications of optimal control to aerospace problems with a focus on modern geometric optimal control tools and numerical continuation techniques. Geometric optimal control is a theory combining optimal control with various concepts of differential geometry. The ultimate objective is to derive optimal synthesis results for general classes of control systems. Continuation or homotopy methods consist in solving a series of parameterized problems, starting from a simple one to end up by continuous deformation with the initial problem. They help overcoming the difficult initialization issues of the shooting method. The combination of geometric control and homotopy methods improves the traditional techniques of optimal control theory.A nonacademic example of optimal attitude-trajectory control of (classical and airborne) launch vehicles, treated in details, illustrates how geometric optimal control can be used to analyze finely the structure of the extremals. This theoretical analysis helps building an efficient numerical solution procedure combining shooting methods and numerical continuation. Chattering is also analyzed and it is shown how to deal with this issue in practice.