多约束条件下的最优两脉冲空间拦截

谢力; 张奕群; 徐俊艳

doi:10.1631/FITEE.1800763

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多约束条件下的最优两脉冲空间拦截

常规文章 | Updated：2022-05-19

- 多约束条件下的最优两脉冲空间拦截
- Optimal two-impulse space interception with multiple constraints
- 信息与电子工程前沿（英文） 2020年21卷第7期页码：1085-1107
- 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 XIE, E-mail: lixie@ncepu.edu.cn
  [ "Yi-qun ZHANG, E-mail: yiqunzhang@hotmail.com" ]
  [ "Jun-yan XU, E-mail: junyan_Xu@sina.cn" ]
- Funds：
  
  Project supported by the National Natural Science Foundation of China (No. 61374084)
- DOI：10.1631/FITEE.1800763
  中图分类号： O232
- 收稿：2018-12-05，
  
  修回：2020-;3-;6，
  
  纸质出版：2020-07
- Accepted：
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谢力, 张奕群, 徐俊艳. 多约束条件下的最优两脉冲空间拦截[J]. 信息与电子工程前沿（英文）, 2020,21(7):1085-1107.

Li XIE, Yi-qun ZHANG, Jun-yan XU. Optimal two-impulse space interception with multiple constraints[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(7): 1085-1107.
谢力, 张奕群, 徐俊艳. 多约束条件下的最优两脉冲空间拦截[J]. 信息与电子工程前沿（英文）, 2020,21(7):1085-1107. DOI： 10.1631/FITEE.1800763.

Li XIE, Yi-qun ZHANG, Jun-yan XU. Optimal two-impulse space interception with multiple constraints[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(7): 1085-1107. DOI： 10.1631/FITEE.1800763.

摘要

本文研究多约束条件下的最优两脉冲空间拦截问题。对空间拦截器的末端位置、脉冲和拦截时刻以及速度脉冲的分量大小施加多约束。通过变分法将这些优化问题归结为多点边值问题。为使用拉格朗日乘子法，采用松弛变量法将所有不等式约束转化为等式约束。为此提出一种新的动态松弛变量法，并建立一种间接优化方法。随后，用所提方法解决自由飞行弹道导弹的两脉冲空间拦截问题。在高精度数值解基础上，得到一些局部最优解的结论。具体来说，通过数值算例，证明了当存在时间和速度脉冲约束时，多约束拦截问题可能出现最优两脉冲解；如果两个脉冲时刻是自由的，那么具有速度脉冲约束的两脉冲空间拦截问题可能退化为单脉冲情形。

Abstract

We consider optimal two-impulse space interception problems with multiple constraints. The multiple constraints are imposed on the terminal position of a space interceptor

impulse and impact instants

and the component-wise magnitudes of velocity impulses. These optimization problems are formulated as multi-point boundary value problems and solved by the calculus of variations. Slackness variable methods are used to convert all inequality constraints into equality constraints so that the Lagrange multiplier method can be used. A new dynamic slackness variable method is presented. As a result

an indirect optimization method is developed. Subsequently

our method is used to solve the two-impulse space interception problems of free-flight ballistic missiles. A number of conclusions for local optimal solutions have been drawn based on highly accurate numerical solutions. Specifically

by numerical examples

we show that when time and velocity impulse constraints are imposed

optimal two-impulse solutions may occur; if two-impulse instants are free

then a two-impulse space interception problem with velocity impulse constraints may degenerate to a one-impulse case.

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