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Sampled-data based average consensus with measurement noises: convergence analysis and uncertainty principle

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Abstract

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.

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Authors and Affiliations

  1. Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Tao Li & JiFeng Zhang

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  1. Tao Li
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  2. JiFeng Zhang
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Correspondence to JiFeng Zhang.

Additional information

Supported by Singapore Millennium Foundation and the National Natural Science Foundation of China (Grant Nos. 60821091, 60674308)

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Li, T., Zhang, J. Sampled-data based average consensus with measurement noises: convergence analysis and uncertainty principle. Sci. China Ser. F-Inf. Sci. 52, 2089–2103 (2009). https://doi.org/10.1007/s11432-009-0177-7

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  • DOI: https://doi.org/10.1007/s11432-009-0177-7

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