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

Authors: Fei Chen, Zengqiang Chen, Zhongxin Liu, Linying Xiang, Zhuzhi Yuan

Addresses: 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

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.

Keywords: consensus; multi-agent systems; MAS; multiple leaders; graph Laplacian; agent-based systems; local rules; complex systems; switching topology; weighted graphs; group decisions; decision making; nearest neighbour; autonomous agents; weighted directed networks.

DOI: 10.1504/IJSCC.2008.021124

International Journal of Systems, Control and Communications, 2008 Vol.1 No.2, pp.227 - 239

Published online: 04 Nov 2008 *

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