Resilient multi-dimensional consensus in adversarial environment

This paper considers the multi-dimensional consensus in networked systems, where some of agents might be misbehaving (or faulty). Despite influence these misbehaviors, benign aim to reach an agreement while avoiding being seriously influenced by faulty ones. To this end, first a general class algorithms, each agent computes “auxiliary point” based on received values and moves its state towards point. Concerning generic form, we present conditions for achieving resilient obtain lower bound exponential convergence rate. Assuming that number malicious is upper bounded, two specific algorithms are further developed obtained conditions. Particularly, solution, Helly’s Theorem, achieves within convex hull formed agents’ initial states, auxiliary point can efficiently computed through linear programming. On other hand, second algorithm serves as “built-in” security guarantee standard average sense performance coincides exactly with ones absence nodes also resisting serious adversarial environment. Some numerical examples provided end verify theoretical results.