Hohmann transfer via constrained optimization

Li XIE; Yi-qun ZHANG; Jun-yan XU

doi:10.1631/FITEE.1800295

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Hohmann transfer via constrained optimization

Regular Papers | Updated：2022-05-19

- Hohmann transfer via constrained optimization
- 约束优化下的霍曼转移
- Frontiers of Information Technology & Electronic Engineering Vol. 19, Issue 11, Pages: 1444-1458(2018)
- Affiliations：
  
  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
  Beijing Institute of Electronic Systems Engineering, Beijing 100854, China
- Author bio：
  
  Li XI, E-mail: lixie@ncepu.edu.cn
  [ "Yi-qun ZHANG, E-mail:yiqunzhang@hotmail.com" ]
  [ "Jun-yan XU, E-mail:junyan_Xu@sina.cn" ]
- Funds：
- DOI：10.1631/FITEE.1800295
  CLC： O232;V412.4
- Received：11 May 2018，
  
  Revised：2018-11-27，
  
  Published：2018-11
- Accepted：
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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.
DOI：

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. DOI： 10.1631/FITEE.1800295.

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。

Abstract

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.

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