第16卷第2期 智能系统学报 Vol.16 No.2 2021年3月 CAAI Transactions on Intelligent Systems Mar.2021 D0:10.11992/tis.202002017 网络出版地址：https:/ns.cnki.net/kcms/detail/23.1538.TP.20201115.1732.002.html 基于博弈论的预警卫星系统抗毁性研究 齐小刚，陈春绮，熊伟2，刘立芳3 (1.西安电子科技大学数学与统计学院，陕西西安710071；2.航天工程大学复杂电子系统仿真技术国防科技 重点实验室，北京101416,3.西安电子科技大学计算机学院，陕西西安710071) 摘要：预警卫星系统在弹道导弹预警方面发挥着重要的作用，一旦受到攻击，将造成重大损失。针对这一实 际情况，利用博弈论知识，将预警卫星系统的攻防过程构建为静态博弈模型。提出攻防状态下刻画系统抗毁性 的方法，将其分为防御者抗毁性和攻击者抗毁性，在完全信息和不完全信息情况下，分析双方应采取的策略， 用仿真得到的容量数据刻画节点受攻击后的失效概率，提出基于仿真数据的攻防策略。并根据仿真数据分析 提出不完全信息下模型的优化方向。 关键词：预警卫星；攻防博弈论：博弈模型；系统抗毁性；防御者抗毁性；攻击者抗毁性；攻击策略；防御策略 中图分类号：TP39:TJ861文献标志码：A文章编号：1673-4785(2021)02-0338-08 中文引用格式：齐小刚，陈春绮，熊伟，等.基于博弈论的预警卫星系统抗毁性研究.智能系统学报，202116(2)：338-345， 英文引用格式：QI Xiaogang,CHEN Chunqi,,XIONG Wei,etal.Research on the invulnerability of an early warning satellite sys- tem based on game theory[Jl.CAAI transactions on intelligent systems,2021,16(2):338-345. Research on the invulnerability of an early warning satellite system based on game theory QI Xiaogang',CHEN Chunqi',XIONG Wei,LIU Lifang' (1.School of Mathematics and Statistics,Xidian University,Xi'an 710071,China;2.Science and Technology on Complex Electron- ic System Simulation Laboratory,Space Engineering University,Beijing 101416,China;3.School of Computer Science and Techno- logy,Xidian University,Xi'an 710071,China) Abstract:Satellite systems play an important role in the early warning of ballistic missile attacks,which may cause heavy losses.In view of this actual situation,using the knowledge of game theory,the attack and defense processes of the early warning satellite system are constructed as a static game model.A method is proposed to characterize the in- vulnerability of the system in the attack and defense states,and then it is divided into defender invulnerability and at- tacker indestructibility.In the case of complete information and incomplete information,the strategies that both sides should adopt are analyzed.The capacity data obtained from simulations is used to characterize the failure probability of the node under attack,and the attack and defense strategies are proposed based on the simulation data.The optimization direction of the model under incomplete information is proposed according to the analysis of simulation data. Keywords:early warning satellite;attack and defense game theory;game model;system invulnerability;defender invul- nerability;attacker invulnerability;attack strategy;defensive strategy 自1957年苏联成功发射第一颗人造地球卫 领域。预警卫星，又称为导弹预警卫星，是天基 星以来，人类进入航天时代，卫星被广泛应用于 预警系统的核心组成部分，主要利用星上红外探 科学探测和研究、天气预报、通信、导航、军事等 测器和可见光探测器，探测导弹尾焰及弹体辐 收稿日期：2020-02-25.网络出版日期：2020-11-16 射，跟踪、识别导弹从发射到助推段、自由段和再 基金项目：国家自然科学基金项目(61877067)：装备领域基金 入段的过程，测量来袭导弹的发射时间、发射地 项目(61420100201162010002-2). 通信作者：陈春绮.E-mail:1098356554@qq.com, 点、攻击目标、飞行方向等参数，提供给地面拦截DOI: 10.11992/tis.202002017 网络出版地址: https://kns.cnki.net/kcms/detail/23.1538.TP.20201115.1732.002.html 基于博弈论的预警卫星系统抗毁性研究 齐小刚1 ，陈春绮1 ，熊伟2 ，刘立芳3 （1. 西安电子科技大学 数学与统计学院，陕西 西安 710071; 2. 航天工程大学 复杂电子系统仿真技术国防科技 重点实验室，北京 101416; 3. 西安电子科技大学 计算机学院，陕西 西安 710071） 摘 要：预警卫星系统在弹道导弹预警方面发挥着重要的作用，一旦受到攻击，将造成重大损失。针对这一实 际情况，利用博弈论知识，将预警卫星系统的攻防过程构建为静态博弈模型。提出攻防状态下刻画系统抗毁性 的方法，将其分为防御者抗毁性和攻击者抗毁性，在完全信息和不完全信息情况下，分析双方应采取的策略， 用仿真得到的容量数据刻画节点受攻击后的失效概率，提出基于仿真数据的攻防策略。并根据仿真数据分析 提出不完全信息下模型的优化方向。 关键词：预警卫星；攻防博弈论；博弈模型；系统抗毁性；防御者抗毁性；攻击者抗毁性；攻击策略；防御策略 中图分类号：TP39；TJ861 文献标志码：A 文章编号：1673−4785(2021)02−0338−08 中文引用格式：齐小刚, 陈春绮, 熊伟, 等. 基于博弈论的预警卫星系统抗毁性研究 [J]. 智能系统学报, 2021, 16(2): 338–345. 英文引用格式：QI Xiaogang, CHEN Chunqi, XIONG Wei, et al. Research on the invulnerability of an early warning satellite sys￾tem based on game theory[J]. CAAI transactions on intelligent systems, 2021, 16(2): 338–345. Research on the invulnerability of an early warning satellite system based on game theory QI Xiaogang1 ，CHEN Chunqi1 ，XIONG Wei2 ，LIU Lifang3 (1. School of Mathematics and Statistics, Xidian University, Xi’an 710071, China; 2. Science and Technology on Complex Electron￾ic System Simulation Laboratory, Space Engineering University, Beijing 101416, China; 3. School of Computer Science and Techno￾logy, Xidian University, Xi’an 710071, China) Abstract: Satellite systems play an important role in the early warning of ballistic missile attacks, which may cause heavy losses. In view of this actual situation, using the knowledge of game theory, the attack and defense processes of the early warning satellite system are constructed as a static game model. A method is proposed to characterize the in￾vulnerability of the system in the attack and defense states, and then it is divided into defender invulnerability and at￾tacker indestructibility. In the case of complete information and incomplete information, the strategies that both sides should adopt are analyzed. The capacity data obtained from simulations is used to characterize the failure probability of the node under attack, and the attack and defense strategies are proposed based on the simulation data. The optimization direction of the model under incomplete information is proposed according to the analysis of simulation data. Keywords: early warning satellite; attack and defense game theory; game model; system invulnerability; defender invul￾nerability; attacker invulnerability; attack strategy; defensive strategy 自 1957 年苏联成功发射第一颗人造地球卫 星以来，人类进入航天时代，卫星被广泛应用于 科学探测和研究、天气预报、通信、导航、军事等 领域。预警卫星，又称为导弹预警卫星，是天基 预警系统的核心组成部分，主要利用星上红外探 测器和可见光探测器，探测导弹尾焰及弹体辐 射，跟踪、识别导弹从发射到助推段、自由段和再 入段的过程，测量来袭导弹的发射时间、发射地 点、攻击目标、飞行方向等参数，提供给地面拦截 收稿日期：2020−02−25. 网络出版日期：2020−11−16. 基金项目：国家自然科学基金项目 (61877067)；装备领域基金 项目（61420100201162010002-2）. 通信作者：陈春绮. E-mail：1098356554@qq.com. 第 16 卷第 2 期 智 能 系 统 学 报 Vol.16 No.2 2021 年 3 月 CAAI Transactions on Intelligent Systems Mar. 2021