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Journal Articles Automatica Year : 2023

A Design Method of Distributed Algorithms via Discrete-time Blended Dynamics Theorem

Abstract

We develop a discrete-time version of the blended dynamics theorem for the use of designing distributed computation algorithms. The blended dynamics theorem enables to predict the behavior of heterogeneous multi-agent systems. Therefore, once we get a blended dynamics for a particular computational task, design idea of node dynamics for individual heterogeneous agents can easily occur. In the continuous-time case, prediction by blended dynamics was enabled by high coupling gain among neighboring agents. In the discrete-time case, we propose an equivalent action, which we call multi-step coupling in this paper. Compared to the continuous-time case, the blended dynamics can have more variety depending on the coupling matrix. This benefit is demonstrated with three applications; distributed estimation of network size, distributed computation of the PageRank, and distributed computation of the degree sequence of a graph, which correspond to the coupling by doubly-stochastic, column-stochastic, and row-stochastic matrices, respectively.
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hal-04235062 , version 1 (10-10-2023)

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Jeong Woo Kim, Jin Gyu Lee, Donggil Lee, Hyungbo Shim. A Design Method of Distributed Algorithms via Discrete-time Blended Dynamics Theorem. Automatica, In press. ⟨hal-04235062⟩
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