摘要
研究带有切换网络结构的网络演化博弈同步问题.首先,利用矩阵半张量积方法,给出局势演化方程的代数化表达式,并得到一个充分必要的代数条件来验证切换网络演化博弈是否与一个静态网络演化博弈达到同步;然后,通过构造一个辅助系统并使用最大不变子集的方法,将切换网络演化博弈的同步问题转化为辅助系统的集合稳定性,提出一个易于验证的充分必要条件,并给出达到同步时最短时间的计算公式;此外,将所得结果推广到局势受限的情况,提出局部同步的概念,并讨论切换网络演化博弈的局部同步问题;最后,通过实例验证理论结果的有效性.
This paper investigates the synchronization problem of networked evolutionary games(NEGs)with switched networked structures.Firstly,the algebraic expression of the strategy profile dynamics is given by using the semi-tensor product(STP)of matrices,and a necessary and sufficient algebraic condition is presented to verify whether a switched NEG is synchronized to a static NEG.Then by constructing an auxiliary system and using the invariant subset-based method,the synchronization problem of switched NEGs can be converted into set stability of the auxiliary system with respect to a given nonempty subset.An easily verifiable necessary and sufficient condition is proposed and the formula is provided to calculate the shortest time.In addition,we extend the obtained results to local synchronization of incompleteprofile switched NEGs.Finally,an illustrative example is given to show the effectiveness of the theoretical results.
作者
王元华
张秋童
臧文科
WANG Yuan-hua;ZHANG Qiu-tong;ZANG Wen-ke(Business School,Shandong Normal University,Ji’nan 250014,China;Institute of Dynamics and Control Science,Shandong Normal University,Ji’nan 250014,China)
出处
《控制与决策》
EI
CSCD
北大核心
2024年第10期3313-3318,共6页
Control and Decision
基金
国家自然科学基金项目(62373230,61903236,62073202)。
关键词
切换网络演化博弈
同步
矩阵半张量积
集合稳定性
不变子集
受限局势
switched networked evolutionary games
synchronization
semi-tensor product of matrices
set stability
invariant subset
incomplete-profile
