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On-line Access: 2018-12-14

Received: 2018-05-11

Revision Accepted: 2018-07-23

Crosschecked: 2018-11-27

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Li Xie


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Frontiers of Information Technology & Electronic Engineering  2018 Vol.19 No.11 P.1444-1458


Hohmann transfer via constrained optimization

Author(s):  Li Xie, Yi-qun Zhang, Jun-yan Xu

Affiliation(s):  State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China; more

Corresponding email(s):   lixie@ncepu.edu.cn, yiqunzhang@hotmail.com, junyan_Xu@sina.cn

Key Words:  Hohmann transfer, Nonlinear programming, Constrained optimization, Calculus of variations

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Li Xie, Yi-qun Zhang, Jun-yan Xu. Hohmann transfer via constrained optimization[J]. Frontiers of Information Technology & Electronic Engineering, 2018, 19(11): 1444-1458.

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A1 - Li Xie
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A1 - Jun-yan Xu
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Inspired by the geometric method proposed by Jean-Pierre MAREC, we first consider the hohmann transfer problem between two coplanar circular orbits as a static nonlinear programming problem with an inequality constraint. By the Kuhn-Tucker theorem and a second-order sufficient condition for minima, we analytically prove the global minimum of the hohmann transfer. Two sets of feasible solutions are found: one corresponding to the hohmann transfer is the global minimum and the other is a local minimum. We next formulate the hohmann transfer problem as boundary value problems, which are solved by the calculus of variations. The two sets of feasible solutions are also found by numerical examples. Via static and dynamic constrained optimizations, the solution to the hohmann transfer problem is re-discovered, and its global minimum is analytically verified using nonlinear programming.


摘要:在Jean-Pierre MAREC几何方法启发下,将两共面圆轨道之间的霍曼转移问题定义为一个不等式约束下的静态非线性规划问题。利用Kuhn-Tucker定理和最小值点存在的一个二阶充分条件,证明霍曼转移的全局最小性。该约束优化问题存在两组可行解,其中对应于霍曼转移的一个解是全局极小值点,另一个解是局部极小值点。随后将霍曼转移问题考虑为有约束的动态优化问题,并用变分法转化为边值问题求解。在静态和动态优化数值算例中验证了静态优化解析给出的两组可行解。由静态和动态约束优化,我们重新发现霍曼转移问题的解,并用非线性规划解析证明了其全局最小性。


Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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