This work studies consensus networks over finite fields, where agents process and communicate values from the set of integers f0; : : : ; p 1g, for some prime number p, and operations are performed modulo p. For consensus networks over finite fields we provide necessary and sufficient conditions on the network topology and weights to ensure convergence. For instance we show that, differently from the case of consensus networks over the field of real numbers, consensus networks over finite fields converge in finite time, and that properties of the agents interaction graph are not sufficient to ensure finitefield consensus. Finally, we discuss the application of finite-field consensus to distributed averaging in sensor networks.

Finite-Field Consensus / Pasqualetti, F.; Borra, Domenica; Bullo, F.. - ELETTRONICO. - (2013). ((Intervento presentato al convegno 52nd IEEE Conference on Decision and Control (CDC 2013) tenutosi a Florence, Italy nel December 10-13, 2013.

Finite-Field Consensus

BORRA, DOMENICA;
2013

Abstract

This work studies consensus networks over finite fields, where agents process and communicate values from the set of integers f0; : : : ; p 1g, for some prime number p, and operations are performed modulo p. For consensus networks over finite fields we provide necessary and sufficient conditions on the network topology and weights to ensure convergence. For instance we show that, differently from the case of consensus networks over the field of real numbers, consensus networks over finite fields converge in finite time, and that properties of the agents interaction graph are not sufficient to ensure finitefield consensus. Finally, we discuss the application of finite-field consensus to distributed averaging in sensor networks.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2522439
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