JZUS - Journal of Zhejiang University SCIENCE

Frontiers of Information Technology & Electronic Engineering 2020 Vol.21 No.7 P.1085-1107

Optimal two-impulse space interception with multiple constraints

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: Space interception problems, Variational method, Multiple constraints, Two-velocity impulses, Multi-point boundary value problems, Local optimal solutions, Dynamic slackness variable method

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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.

多约束条件下的最优两脉冲空间拦截

谢力¹，张奕群²，徐俊艳²
¹华北电力大学控制与计算机工程学院新能源电力系统国家重点实验室，中国北京市，102206
²北京电子工程总体研究所，中国北京市，100854

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。

关键词：空间拦截问题；变分法；多约束；两速度脉冲；多点边值问题；局部最优解；动态松弛变量法

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