基于事件驱动控制的混杂动态博弈系统的纳什均衡分析  

Nash equilibrium analysis of hybrid dynamic games system based on event-triggered control

作　　者：陈向勇 曹进德 赵峰 姜晓伟 CHEN Xiang-yong;CAO Jin-de;ZHAO Feng;JIANG Xiao-wei(School of Automation and Electrical Engineering,Linyi University,Linyi Shandong 276005,China;School of Mathematics,Southeast University,Nanjing Jiangsu 211189,China;Hubei Key Laboratory of Advanced Control and Intelligent Automation of Complex Systems,School of Automation,China University of Geosciences,Wuhan Hubei 430074,China)

机构地区：[1]临沂大学自动化与电气工程学院,山东临沂276005 [2]东南大学数学学院,江苏南京211189 [3]中国地质大学,复杂系统先进控制与智能自动化湖北省重点实验室,自动化学院,湖北武汉430074

出　　处：《控制理论与应用》2021年第11期1801-1808,共8页Control Theory & Applications

基　　金：国家自然科学基金项目(12026235,12026234,62173175);高等学校学科创新引智计划项目(B17040);山东省自然科学基金项目(ZR2019BF045,ZR2019MF021,ZR2019QF004);山东省高等学校科研计划项目(J18KA354)。

摘　　要：本文研究了基于事件驱动控制的混杂动态博弈系统的纳什均衡分析问题.首先,分析了事件驱动机制对混杂动态博弈过程的影响,进而,在进行状态空间描述的基础上,给出了混杂动态博弈的纳什均衡的定义,并建立了对应博弈系统的策略型模型.其次,结合Lanchester方程,分别讨论了两类混杂动态博弈系统的均衡问题,包括事件驱动策略设计和固定的情况,获得了均衡解存在的必要条件.最后,通过数值模拟进行了应用分析,验证了所取得结果的合理性和科学性,并总结了混杂动态博弈研究的未来工作.This paper studies the Nash equilibrium analysis and application of event-triggered hybrid dynamic games system.Firstly,we consider the influence of event driven mechanism on the process of hybrid dynamic games.Then,by summarizing the state space model of hybrid dynamic games,the definition of Nash equilibrium is given,and the strategic model of corresponding game system is established.Secondly,combined with Lanchester equation,the equilibrium problems of two kinds of event driven hybrid dynamic games are discussed,including event driven strategy design and fixed case,and the necessary conditions for the existence of equilibrium solutions are obtained.Finally,the application analysis is carried out through numerical simulation,which verifies the rationality and scientificity of the results,and summarizes the future research work of hybrid dynamic games.

关 键 词：事件驱动控制 混杂动态博弈 纳什均衡 LANCHESTER方程 

分 类 号：O225[理学—运筹学与控制论]