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Zbl 1185.93006
Li, Tao; Zhang, Ji-Feng
Mean square average-consensus under measurement noises and fixed topologies: necessary and sufficient conditions. (English)
[J] Automatica 45, No. 8, 1929-1936 (2009). ISSN 0005-1098

Summary: An average-consensus control is considered for networks of continuous-time integrator agents under fixed and directed topologies. The control input of each agent can only use its local state and the states of its neighbors corrupted by white noises. To attenuate the measurement noises, time-varying consensus gains are introduced in the consensus protocol. By combining the tools of algebraic graph theory and stochastic analysis, the convergence of these kinds of protocols is analyzed. Firstly, for noise-free cases, necessary and sufficient conditions are given on the network topology and consensus gains to achieve average-consensus. Secondly, for the cases with measurement noises, necessary and sufficient conditions are given on the consensus gains to achieve asymptotic unbiased mean square average-consensus. It is shown that under the protocol designed, all agents' states converge to a common Gaussian random variable, whose mathematical expectation is just the average of the initial states.

MSC 2000:: *93A14 Decentralized systems
93B50 Synthesis problems
93E03 General theory of stochastic systems
93E10 Estimation and detection in stochastic control

Keywords: multi-agent systems; average-consensus; distributed coordination; distributed estimation; stochastic systems

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Zentralblatt MATH Berlin [Germany]