Synchronization of networks over finite fields
In this paper, the synchronization problem for networks over finite fields is investigated, which is a generalization of consensus and provides a new perspective for networks of agents with limited capacities of memory and communication. It is assumed that the states and communication weights can on...
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sg-ntu-dr.10356-1520982021-09-08T01:48:13Z Synchronization of networks over finite fields Meng, Min Li, Xiuxian Xiao, Gaoxi School of Electrical and Electronic Engineering Engineering::Electrical and electronic engineering Synchronization Networks In this paper, the synchronization problem for networks over finite fields is investigated, which is a generalization of consensus and provides a new perspective for networks of agents with limited capacities of memory and communication. It is assumed that the states and communication weights can only attain values from a finite alphabet equipped with a prime number of integers, termed finite fields, and operations are processed relying on modular arithmetic. For this synchronization problem, necessary and sufficient conditions are derived based on the transition graph of the studied network. The large number of nodes in the transition graph, dependent on the numbers of integers in finite fields and the agents, may lead to high computational cost and difficulties in verifying synchronization. To avoid this, an equivalent condition for synchronization of networks is provided by the characteristic polynomial of the studied network matrix. Furthermore, in a synchronized network over finite fields, the periodic behavior can be determined by the network matrix and the initial state. Ministry of Education (MOE) The work was partially supported by Ministry of Education, Singapore under contract of MOE2016-T2-1-119. 2021-09-08T01:48:13Z 2021-09-08T01:48:13Z 2020 Journal Article Meng, M., Li, X. & Xiao, G. (2020). Synchronization of networks over finite fields. Automatica, 115, 108877-. https://dx.doi.org/10.1016/j.automatica.2020.108877 0005-1098 https://hdl.handle.net/10356/152098 10.1016/j.automatica.2020.108877 2-s2.0-85079033324 115 108877 en MOE2016-T2-1-119 Automatica © 2020 Elsevier Ltd. All rights reserved. |
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Engineering::Electrical and electronic engineering Synchronization Networks Meng, Min Li, Xiuxian Xiao, Gaoxi Synchronization of networks over finite fields |
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In this paper, the synchronization problem for networks over finite fields is investigated, which is a generalization of consensus and provides a new perspective for networks of agents with limited capacities of memory and communication. It is assumed that the states and communication weights can only attain values from a finite alphabet equipped with a prime number of integers, termed finite fields, and operations are processed relying on modular arithmetic. For this synchronization problem, necessary and sufficient conditions are derived based on the transition graph of the studied network. The large number of nodes in the transition graph, dependent on the numbers of integers in finite fields and the agents, may lead to high computational cost and difficulties in verifying synchronization. To avoid this, an equivalent condition for synchronization of networks is provided by the characteristic polynomial of the studied network matrix. Furthermore, in a synchronized network over finite fields, the periodic behavior can be determined by the network matrix and the initial state. |
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School of Electrical and Electronic Engineering |
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School of Electrical and Electronic Engineering Meng, Min Li, Xiuxian Xiao, Gaoxi |
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Article |
author |
Meng, Min Li, Xiuxian Xiao, Gaoxi |
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Meng, Min |
title |
Synchronization of networks over finite fields |
title_short |
Synchronization of networks over finite fields |
title_full |
Synchronization of networks over finite fields |
title_fullStr |
Synchronization of networks over finite fields |
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Synchronization of networks over finite fields |
title_sort |
synchronization of networks over finite fields |
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2021 |
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https://hdl.handle.net/10356/152098 |
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1710686944413876224 |