Distributed consensus on boolean information

Fagiolini, Adriano and Martini, Simone and Dubbini, Nevio and Bicchi, Antonio (2009) Distributed consensus on boolean information. In: 1st IFAC Workshop on Estimation and Control of Networked Systems (NecSys'09), 24-26 settembre 2009, Venice, Italy.

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Abstract

In this paper we study the convergence towards consensus on information in a distributed system of agents communicating over a network. The particularity of this study is that the information on which the consensus is seeked is not represented by real numbers, rather by logical values or compact sets. Whereas the problems of allowing a network of agents to reach a consensus on logical functions of input events, and that of agreeing on set{valued information, have been separately addressed in previous work, in this paper we show that these problems can indeed be attacked in a unied way in the framework of Boolean distributed information systems. Based on a notion of contractivity for Boolean dynamical systems, a necessary and sucient condition ensuring the global convergence toward a unique equilibrium point is presented. This result can be seen as a rst step toward the denition of a unied framework to uniformly address all consensus problems on Boolean algebras.

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