[an error occurred while processing this directive] [an error occurred while processing this directive] [an error occurred while processing this directive]
[an error occurred while processing this directive]

弹箭与制导学报 >

2023 , Vol. 43 >Issue 4: 39 - 45

DOI: https://doi.org/10.15892/j.cnki.djzdxb.2023.04.006

基于零和微分对策的非仿射导弹拦截系统制导律设计

  • 田辈辈 1 ,
  • 刘奇 1 ,
  • 袁斐然 2
展开
  • 1 焦作大学机电工程学院,河南 焦作 454003
  • 2 航空电子系统综合技术重点实验室,上海 200233

田辈辈(1991—),女,助教,硕士,研究方向:自适应动态规划,鲁棒控制,最优控制研究。

收稿日期: 2022-10-26

  网络出版日期: 2025-02-07

基金资助

河南省科技计划项目(212400410356)

收起

Design of Guidance Law for Non-affine Missile Interception System Based on Zero-sum Differential Game

  • TIAN Beibei 1 ,
  • LIU Qi 1 ,
  • YUAN Feiran 2
Expand
  • 1 College of Mechanical and Electronic Engineering,Jiaozuo University,Jiaozuo 454003,Henan, China
  • 2 Key Laboratory of Science and Technology on Avionics Integration Technologies,Shanghai 200233,China

Received date: 2022-10-26

  Online published: 2025-02-07

Fold

摘要

文中基于零和微分对策理论研究了非仿射导弹拦截系统制导律设计问题。首先构建辅助系统,将系统转化为仿射非线性增广形式;其次将导弹与目标视为对抗双方,根据极大极小值原理,设计最优微分对策制导策略,使得拦截系统能够满足预设的性能指标;接着为了获得HJI(Hamilton-Jacobi-Isaacs)方程解析解,利用积分自适应动态规划技术构建神经网络;然后设计积分型自适应权值更新律,在线学习最优微分对策制导律,通过Lyapunov方法证明了闭环系统的有界性;最后将所提算法应用于非仿射导弹拦截系统。仿真结果表明,导弹视线角速率和相对速率满足目标成功捕获必要条件且脱靶量为1 m左右,导弹能够成功拦截目标。

关键词： 零和微分对策; 非仿射导弹拦截系统; 积分自适应动态规划; 神经网络

本文引用格式

田辈辈 , 刘奇 , 袁斐然 . 基于零和微分对策的非仿射导弹拦截系统制导律设计[J]. 弹箭与制导学报, 2023 , 43(4) : 39 -45 . DOI: 10.15892/j.cnki.djzdxb.2023.04.006

Abstract

In this paper, the problem of guidance law of non-affine missile interception system is studied based on zero-sum differential game theory. Firstly, an auxiliary system is constructed and the system is converted into affine nonlinear augmented form. Secondly, the missile and target are regarded as competitors and the optimal differential game guidance strategy is designed based on the maximin principle to make the system meet the predefined performance index function. Subsequently, to obtain the analytical solution of the HJI(Hamilton-Jacobi-Isaacs) equation, the integral adaptive dynamic programming technique is used to develop the neural network. Then, the integral adaptive weight updating law is designed to learn the optimal differential game guidance law online and the closed-loop system is proved to be bounded by Lyapunov theory. Finally, the proposed method is applied to the non-affine missile interception system. The simulation results indicate that the line of sight angle rate and range rate satisfy the necessary condition for successful target capture. In addition, the minimum terminal zero effort miss distance is about 1 m. These demonstrate that the target can be intercepted successfully and the proposed method is effective, the missile can successfully intercept the maneuvering target and the proposed algorithm is shown its effectiveness.

Key words： zero-sum differential game; non-affine missile interception system; integral adaptive dynamic programming; neural network

[an error occurred while processing this directive]

参考文献

原文顺序 | 文献年度倒序 | 文中引用次数倒序
[1]
郝丽娜, 曹瑞珉, 王风立, 等. 导弹拦截的混杂对策系统建模研究[J]. 东北大学学报(自然科学版), 2018, 39(7): 931-936.

DOI

HAO L N, CAO R M, WANG F L, et al. Modeling of hybrid game system for missile interception[J]. Journal of Northeastern University (Natural Science), 2018, 39(7): 931-936.

[2]
LI Z, XIA Y, SU C Y, et al. Missile guidance law based on robust model predictive control using neural-network optimization[J]. IEEE Transactions on Neural Networks & Learning Systems, 2017, 26(8): 1803-1809.

[3]
程建良, 葛爱东, 吕琳琳. 美国导弹防御系统解析[J]. 飞航导弹, 2020(6): 55-58.

CHENG J L, GE A D, LYU L L. Analysis of american missile defense system[J]. Aerospace Missiles, 2020(6): 55-58.

[4]
WU P, YANG M. Integrated guidance and control design for missile with terminal impact angle constraint based on sliding mode control[J]. Systems Engineering and Electronics, 2012(4): 623-628.

[5]
KIM H G, LEE J Y, KIM H J, et al. Look-angle-shaping guidance law for impact angle and time control with field-of-view constraint[J]. IEEE Transactions on Aerospace and Electronic Systems, 2020, 56(2): 1602-1612.

[6]
ZHOU R, SUN X J, WU J, et al. Multi-missile distributed cooperative guidance integrating backstepping sliding mode control[J]. Control and Decision, 2014, 29(9): 1617-1622.

[7]
JI Y, LIN D F, PEI P, et al. Robust partial integrated guidance and control approaches for maneuvering targets[J]. International Journal of Robust and Nonlinear Control, 2019, 29(18): 6522-6541.

[8]
陈圣, 王旭刚. 制导炮弹非线性鲁棒自适应控制系统设计[J]. 电光与控制, 2014, 21(4): 61-64.

CHEN S, WANG X G. Design of nonlinear robust adaptive control system for guided projectile[J]. Electronics Optics and Control, 2014, 21(4): 61-64.

[9]
花文华, 张金鹏. 飞行速度可调导弹的自适应滑模制导律[J]. 电光与控制, 2022, 29(7): 1-5.

HUA W H, ZHANG J P. Adaptive sliding mode guidance law for missiles with adjustable flight velocity[J]. Electronics Optics and Control, 2022, 29(7): 1-5.

[10]
CUI L, NAN J, CHANG S P, et al. Fixed-time ESO based fixed-time integral terminal sliding mode controller design for a missile[J]. ISA Transactions, 2021, 125: 237-251.

DOI PMID

[11]
SUN J, LIU C. Backstepping-based adaptive dynamic programming for missile-target guidance systems with state and input constraints[J]. Journal of the Franklin Institute, 2018, 355(17): 8412-8440.

[12]
黄英博, 吕永峰, 赵刚, 等. 非线性主动悬架系统自适应最优控制[J]. 控制与决策, 2022: 1-9.

HUANG Y B, LYU Y F, ZHAO G, et al. Adaptive optimal control of nonlinear active suspension system[J]. Control and Decision, 2022, 37(12): 3197-3206.

[13]
ISAACS R. Differential games[M]. New York: Wiley Press, 1965.

[14]
DUAN D, LIU C, ZHANG S. Robust optimal control for finite-horizon zero-sum differential games via a plug-n-play event-triggered scheme[J]. Journal of the Franklin Institute, 2020, 357(10): 5989-6017.

[15]
李俊贤, 范军芳. 考虑目标主动防御的空地弹药微分对策制导[J]. 电光与控制, 2022, 29(9): 22-26.

LI J X, FANJ F. Differential game guidance for air-ground munitions considering active target defense[J]. Electronics Optics and Control, 2022, 29(9): 22-26.

[16]
SUN J L, LIU C S, ZHAO X. Backstepping-based zero-sum differential games for missile-target interception systems with input and output constraints[J]. IET Control Theory & Applications, 2019, 12(2): 243-253.

[17]
LI J, SHI Q. Adaptive control for a class of uncertain pure-feedback nonlinear systems using backstepping based on extreme learning machine[J]. Ciesc Journal, 2016, 67(7): 2934-2942.

[18]
黄燕华, 代冀阳, 应进, 等. 带有输入饱和及输出受限非仿射系统固定时间跟踪控制[J]. 控制与决策, 2023, 38(2): 429-434.

HUANG Y H, DAI J Y, YING J, et al. Fixed-time tracking control for non-affine systems with input saturation and output limitation[J]. Control and Decision, 2023, 38(2): 429-434.

[19]
WANG D, QIAO J. Approximate neural optimal control with reinforcement learning for a torsional pendulum device[J]. Neural Networks, 2019, 117(10): 1-7.

[20]
田辈辈, 赵锋. 基于自适应动态规划的鲁棒最优导弹自动驾驶仪滑模控制[J]. 电光与控制, 2021, 28(11): 54-59.

TIAN B B, ZHAO F. Robust optimal sliding mode control of missile autopilot based on adaptive dynamic programming[J]. Electronics Optics and Control, 2021, 28(11): 54-59.

[21]
GARCIA E, CASBEER D W, PACHTER M. Cooperative strategies for optimal aircraft defense from an attacking missile[J]. Journal of Guidance Control & Dynamics, 2015, 28(8): 1510-1520.

Options
文章导航

/

〈 〉

[an error occurred while processing this directive]