The Laplacian of a graph mathematically formalizes the interactions occurring between nodes/agents connected by a link. Its extension to account for the indirect peer influence through longer paths, weighted as a function of their length, is represented by the notion of transformed d-path Laplacians. In this paper, we propose a second-order consensus protocol based on these matrices and derive criteria for the stability of the error dynamics, which also consider the presence of a communication delay. We show that the new consensus protocol is stable in a wider region of the control gains, but admits a smaller maximum delay than the protocol based on the classical Laplacian. We show numerical examples to illustrate our theoretical results.

Second-order consensus protocols based on transformed d-path Laplacians

Gambuzza, Lucia Valentina;Frasca, Mattia;
2019

Abstract

The Laplacian of a graph mathematically formalizes the interactions occurring between nodes/agents connected by a link. Its extension to account for the indirect peer influence through longer paths, weighted as a function of their length, is represented by the notion of transformed d-path Laplacians. In this paper, we propose a second-order consensus protocol based on these matrices and derive criteria for the stability of the error dynamics, which also consider the presence of a communication delay. We show that the new consensus protocol is stable in a wider region of the control gains, but admits a smaller maximum delay than the protocol based on the classical Laplacian. We show numerical examples to illustrate our theoretical results.
Communication delay; Consensus; d-path Laplacians; Computational Mathematics; Applied Mathematics
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11769/361943
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