Finite-time Average Consensus in a Byzantine Environment Using Set-Valued Observers

Abstract

This paper addresses the problem of consensus in the presence of Byzantine faults, modeled by an attacker injecting a perturbation in the state of the nodes of a network. It is firstly shown that Set-Valued Observers (SVOs) attain finite-time consensus, even in the case where the state estimates are not shared between nodes, at the expenses of requiring large horizons, thus rendering the computation problem intractable in the general case. A novel algorithm is therefore proposed that achieves finite-time consensus, even if the aforementioned requirement is dropped, by intersecting the set-valued state estimates of neighboring nodes, making it suitable for practical applications and enabling nodes to determine a stopping time. This is in contrast with the standard iterative solutions found in the literature, for which the algorithms typically converge asymptotically and without any guarantees regarding the maximum error of the final consensus value, under faulty environments. The algorithm suggested is evaluated in simulation, illustrating, in particular, the finite-time consensus property.