Gossip average consensus in a byzantine environment using stochastic set-valued observers

Abstract — We address the problem of a consensus system in the presence of Byzantine faults seen as an attacker injecting a perturbation in the state of the nodes. We propose the use of Set-Valued Observers to detect if the state observations are compatible with the system dynamics. The method is extended to the stochastic case by introducing a strategy to construct a set that is guaranteed to contain all possible states with, at least, a pre-specified desired probability. The proposed algorithm is stable in the sense that it requires a finite number of vertices to represent polytopic sets while also enabling the a priori computation of the largest magnitude of a disturbance that an attacker can inject without being detected.

D. Silvestre, P. Rosa, R. Cunha, J. P. Hespanha, and C. Silvestre
Proceedings of the 52nd IEEE Conference on Decision and Control
Date: March, 2013
ICB Affiliated Authors: João P Hespanha