How Many Leaders Are Required for Consensus
会议名称：《第二十七届中国控制会议》
会议日期：2008年
学科分类：0711[理学-系统科学] 07[理学] 08[工学] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 071102[理学-系统分析与集成] 081103[工学-系统工程]
基 金：supported by National Nature Science Foundation under Grants 60574068
关 键 词：Leader Consensus Vicsek model Multi-array martingale theorem Neighbor graph
摘 要：Many natural and artificial systems,for example,fish school,bird flocks,robot team,are often composed of two different classes of agents:autonomous agents and *** leaders have pertinent information,such as the location of the food source,while the autonomous agents make decisions according to local *** a basic problem is:how many leaders are required in order to induce all agents move with the same direction as leaders（such collective behavior is called consensus） In this paper,we will consider a simple,but typical model proposed by Vicsek et al.（Vicsek model） ,in addition to the ordinary agents moving at the constant velocity with heading updated according to local rules,we add some leaders at the same velocity but with fixed *** will show that in order to induce the whole system reach consensus,the proportion of the leaders decreases as the number of autonomous agents increases under some conditions on the velocity v and neighborhood radius *** the numerical examples are given to illustrate the necessity of the *** proof is based on the analysis of the system dynamics and the initial neighbor graph,where multi-array martingale theorem play a key role.