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Leitao Gao,Guangshe Zhao,Guoqi Li,Yuming Liu,Jiangshuai Huang,Changyun Wen 제어·로봇·시스템학회 2019 International Journal of Control, Automation, and Vol.17 No.1
In this paper, we consider how to determine the minimum number of leaders with allocation and how toachieve consensus over directed networks consisting of time-varying nonlinear multi-agents. Firstly, the problemof finding minimum number of leaders is formulated as a minimum spanning forest problem, i.e., finding theminimum population of trees in the network. By introducing a toll station connecting with each agent, this problemis converted to a minimum spanning tree problem. In this way, the minimum number of leaders is determined andthese leaders are found locating at the roots of each tree in the obtained spanning forest. Secondly, we describe avirtual leader connected with the allocated leaders, which indicates that the number of edges connected the followeragents with the virtual leader is the least in an arbitrary directed network. This method is different from the existingconsensus problem of redundant leaders or edges that connect the follower with one leader in special networks. A distributed consensus protocol is revisited for achieving final global consensus of all agents. It is theoreticallyshown that such a protocol indeed ensures consensus. Simulation examples in real-life networks are also providedto show the effectiveness of the proposed methodology. Our works enable studying and extending application ofconsensus problems in various complex networks.
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