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On the influence of noise in randomized consensus algorithms

Renato Vizuete 1, 2 Paolo Frasca 1 Elena Panteley 2 
1 DANCE - Dynamics and Control of Networks
Inria Grenoble - Rhône-Alpes, GIPSA-PAD - GIPSA Pôle Automatique et Diagnostic
Abstract : In this paper we study the influence of additive noise in randomized consensus algorithms. Assuming that the update matrices are symmetric, we derive a closed form expression for the mean square error induced by the noise, together with upper and lower bounds that are simpler to evaluate. Motivated by the study of Open Multi-Agent Systems, we concentrate on Randomly Induced Discretized Laplacians, a family of update matrices that are generated by sampling subgraphs of a large undirected graph. For these matrices, we express the bounds by using the eigenvalues of the Laplacian matrix of the underlying graph or the graph's average effective resistance, thereby proving their tightness. Finally, we derive expressions for the bounds on some examples of graphs and numerically evaluate them.
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Submitted on : Wednesday, July 15, 2020 - 4:39:35 PM
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Renato Vizuete, Paolo Frasca, Elena Panteley. On the influence of noise in randomized consensus algorithms. IEEE Control Systems Letters, IEEE, 2021, 5 (3), pp.1025-1030. ⟨10.1109/LCSYS.2020.3009035⟩. ⟨hal-02899936⟩



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