Worst-case performance of rendezvous networks in the presence of adversarial nodes

In this paper, we consider the performance of distributed control algorithms for networked robotic systems when one or more robots fail to execute the optimal policy. In particular, we investigate the performance of the circumcenter algorithm with connectivity maintenance [1]-[3] when one or more adversarial agents act maliciously to maximally disrupt convergence of the remaining, cooperative agents. To this end, we formulate a performance objective for each adversary node in terms of the circumradii of its cooperative neighbors in a communication graph which does not require omniscience of adversaries as is often assumed in the literature (e.g., [4], [5]). We provide an optimization algorithm based on finite-horizon dynamic programming, and obtain solutions through numerical simulation. Our results show that in general adversarial nodes are able not only to impede convergence toward consensus, but can also affect global changes in the topology of the communication graph for the cooperative agents.