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Zbl 1182.93083
Li, Tao; Zhang, Jifeng
Sampled-data based average consensus with measurement noises: convergence analysis and uncertainty principle. (English)
[J] Sci. China, Ser. F 52, No. 11, 2089-2103 (2009). ISSN 1009-2757

Summary: In this paper, sampled-data based average-consensus control is considered for networks consisting of continuous-time first-order integrator agents in a noisy distributed communication environment. The impact of the sampling size and the number of network nodes on the system performances is analyzed. The control input of each agent can only use information measured at the sampling instants from its neighborhood rather than the complete continuous process, and the measurements of its neighbors' states are corrupted by random noises. By probability limit theory and the property of graph Laplacian matrix, it is shown that for a connected network, the static mean square error between the individual state and the average of the initial states of all agents can be made arbitrarily small, provided the sampling size is sufficiently small. Furthermore, by properly choosing the consensus gains, almost sure consensus can be achieved. It is worth pointing out that an uncertainty principle of Gaussian networks is obtained, which implies that in the case of white Gaussian noises, no matter what the sampling size is, the product of the steady-state and transient performance indices is always equal to or larger than a constant depending on the noise intensity, network topology and the number of network nodes.

MSC 2000:: *93C57 Sampled-data control systems
93E03 General theory of stochastic systems
93A14 Decentralized systems

Keywords: multi-agent systems; average consensus; stochastic systems; sampled-data based control; distributed stochastic approximation; uncertainty principle

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