On the security of linear consensus networks

This work considers the problem of reaching consensus in linear networks with misbehaving agents. A solution to this problem is relevant for several tasks in multiagent systems including motion coordination, clock synchronization, and cooperative estimation. By modelling the misbehaving nodes as unknown and unmeasurable inputs affecting the network, we recast the problem into a system theoretic framework. Only relying on their direct measurements, the agents detect and identify uncooperative behaviors using fault detection and isolation techniques. We consider both the cases of Byzantine as well as non-colluding faults, and we express the solvability conditions of the two cases in terms of the observability properties of a linear system associated with the network, and from a graph theoretic perspective. It is shown that generically any node can correctly detect and identify the misbehaving agents, provided that the connectivity of the network is sufficiently high. Precisely, for a linear consensus network to be generically resilient to k concurrent faults, the connectivity of the communication graph needs to be 2k+1, if Byzantine agents are allowed, and k+1, if non-colluding agents are considered.