有向通讯网络下一类动态群体的整体动力学行为  

Global dynamic-behavior of a group of swarms in directed communication network

作　　者：余宏旺[1] 郑毓蕃[2,3] 张宝善[1] 

机构地区：[1]南京审计学院数学与统计学院,江苏南京211815 [2]华东师范大学数学系,上海200062 [3]上海大学数学系,上海200436

出　　处：《控制理论与应用》2011年第9期1091-1098,共8页Control Theory & Applications

基　　金：国家自然科学基金资助项目(60674046);南京审计学院硕士建设点资助项目(202720035)

摘　　要：本文运用图论、矩阵分析和现代控制理论的方法,研究有向通讯网络下一类二维群体的全局动力学行为.此类群体由众多具有相同动力学性质的个体组成,每个个体在不与其他个体发生作用的情况下是李雅普诺夫稳定的,与其他个体交流的信息是传感器测得的带有偏差的位置信息.当每个个体采取分布式线性控制协议时,整个群体的动力学行为,不仅和个体的动力学方程有关,而且和网络结构的代数特征有关.本文具体给出了群体出现全局渐近聚集、周期振荡和发散3种不同行为的代数判据.最后,仿真例子验证了本文结果的有效性.This paper investigates global dynamic-behavior of a group of swarms in directed network by means of graph theory,matrix analysis and control theory.The swarms consist of many identical dynamical agents and each agent is stable in the sense of Lyapunov when it is disconnected from other agents.Each agent communicates the biased position infor-mation with its neighbors.When each dynamical agent employs a linear distributed protocol in communication network,the global dynamic-behaviors of swarms not only depend on the dynamic equations of agents,but also on the algebraic characteristics associated with the network topology.Moreover,algebraic criteria are developed for the agents to achieve gradual aggregation,periodical stability or divergence in trajectories.Finally,the simulation example shows the desired result.

关 键 词：群体 分布式控制协议 动力学行为 赫尔维茨稳定 

分 类 号：O157.5[理学—数学]