王鹏宇a,b 纪志坚a,b 刘祥坤a
青岛大学a.自动化学院;b.系统科学研究院
摘要：针对由任意个连续和离散时间子系统组成的混合多智能体系统，研究了其博弈一致性，证明了博弈参与者的个数与其中根节点的个数之间的关系是一致性实现的充要条件。为使实现一致性的代价最小，基于博弈论方法对子系统之间的交互进行建模并设计了相应的成本函数。同时，证明所设计的博弈存在唯一的纳什均衡，进而得到混合系统实现一致性的充要条件。研究结果表明，博弈参与者与其中根节点的个数是实现博弈一致性的一个新途径，这与现有文献中讨论的由两个子系统组成的混合系统博弈一致性的判定条件不同。
关键词：混合多智能体系统;一致性;博弈论;纳什均衡基金资助：国家自然科学基金(62373205，62033007)； 山东省泰山学者特聘教授人才支持计划(tstp20230624，ts20190930);山东省泰山学者攀登计划![]()
Consensus of First-order
Hybrid Multi-agent Systems Based on Game TheoryWANG Pengyua,b,
JI Zhijiana,b, LIU Xiangkunaa.School of Automation; b.Academy of Systems
Science and Control, Qingdao University, Abstract: For the hybrid
multi-agent system composed of any continuous-time and discrete-time
subsystems, the game consensus is studied for the first time, and it is proved
that the relationship between the number of game participants and the number of
root nodes is a sufficient and necessary condition for the consensus
realization. In order to minimize the cost of achieving consensus, the
interaction between subsystems is modeled based on the game theory and the
corresponding cost function is designed. At the same time, it is proved that
there is a unique Nash equilibrium in the designed game, and then the
sufficient and necessary conditions for the consensus of the hybrid system are
obtained. The results show that the number of game participants and the number
of root nodes is a new way to achieve game consensus, which is different from
the judgment condition of game consensus in a hybrid system composed of two
subsystems discussed in the existing literature.Keywords: hybrid multi-agent systems; consensus; game theory;
Nash equilibrium作者介绍:
第一作者：王鹏宇（2001-），山东潍坊人，硕士研究生，主要研究方向为多智能体网络系统。
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通讯作者：纪志坚（1973-），山东青岛人，博士、二级教授、泰山学者特聘专家。现为博士生导师、山东省杰出青年科学基金获得者、山东省有突出贡献的中青年专家、山东省优秀研究生指导教师；连续入选Elsevier中国高被引学者榜单。入围中国控制理论界的重要奖项“关肇直”奖，是近60名最佳论文奖申请者中的6名入围者之一；以第一位次获得了北京大学的五四奖学金、中国石油奖学金和学术创新奖。主要研究方向为群体智能和多智能体系统协同控制。
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第三作者：刘祥坤（2004-），山东滨州人，本科生，主要研究方向为多智能体网络系统。王鹏宇,纪志坚,刘祥坤. 基于博弈论的一阶混合多智能体系统一致性[DB/OL].(2024-12-09).https://kns.cnki.net/kcms2/article/abstract?v=UbUZFcLhzIL4YuXTUl-5gPqxFTw1PbA6W0aLxeddtHL545pMUZ-4ezsm834Dl9LfxIxNgm5bom1u2Jki3DdrhZbATlt_xgNc1KN-FgqSUD5k0bTEdS-Bp5Y1SfofZBdkc3KFQ1aRD_UbuwPK0bgkzR1C22AlbX69SPfroUd55AFqENxsUJ692zsmFhnjhkkb&uniplatform=NZKPT&language=CHS.
