Convergence of Type-Symmetric and Cut-Balanced Consensus Seeking Systems
Author(s)Hendrickx, Julien; Tsitsiklis, John N.
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We consider continuous-time consensus seeking systems whose time-dependent interactions are cut-balanced, in the following sense: if a group of agents influences the remaining ones, the former group is also influenced by the remaining ones by at least a proportional amount. Models involving symmetric interconnections and models in which a weighted average of the agent values is conserved are special cases. We prove that such systems always converge. We give a sufficient condition on the evolving interaction topology for the limit values of two agents to be the same. Conversely, we show that if our condition is not satisfied, then these limits are generically different. These results allow treating systems where the agent interactions are a priori unknown, being for example random or determined endogenously by the agent values.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
IEEE Transactions on Automatic Control
Institute of Electrical and Electronics Engineers (IEEE)
Hendrickx, Julien M., and John N. Tsitsiklis. “Convergence of Type-Symmetric and Cut-Balanced Consensus Seeking Systems.” IEEE Trans. Automat. Contr. 58, no. 1 (January 2013): 214–218.