Group decision making with multiple leaders: local rules, weighted networks and consensus

Authors:
Fei Chen;Zengqiang Chen;Zhongxin Liu;Linying Xiang;Zhuzhi Yuan
Affiliations:
Department of Automation, Nankai University, Tianjin, 300071, PR China.;Department of Automation, Nankai University, Tianjin, 300071, PR China.;Department of Automation, Nankai University, Tianjin, 300071, PR China.;Department of Automation, Nankai University, Tianjin, 300071, PR China.;Department of Automation, Nankai University, Tianjin, 300071, PR China
Venue:
International Journal of Systems, Control and Communications
Year:
2008

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Abstract

In this paper, a realistic and simple discrete-time model based on nearest neighbour rules for describing the movements of autonomous agents is introduced. Two kinds of networks are considered here: weighted directed networks with fixed topology; weighted directed networks with switching topology. The analysis is based on a blend of graph-theoretic and system-theoretic tools. In addition to the stability analysis, the steady state of convergence is also analysed. It turns out that homogenous digraphs plays a central role in addressing average-consensus problems, where the notation 'leadership' is introduced to measure the influence of a node to the consensus of the group. Finally, numerical examples are included which find very good agreements with the analytical results.