Sampled-data based average consensus with measurement noises: convergence analysis and uncertainty principle |
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Authors: | Tao Li JiFeng Zhang |
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Affiliation: | Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China |
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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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Keywords: | multi-agent systems average consensus stochastic systems sampled-data based control distributed stochastic approximation uncertainty principle |
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