Distributed Multi-Equilibria Consensus in the Presence of Byzantine Adversaries and Time Delays

In this paper, fault tolerant multi-equilibria consensus computation is studied when the thread model is considered as structured Byzantine (StrBYZ). First, a brief review on graph theoretic concepts that we use throughout this paper is provided. Then, the structured Byzantine fault model is presented by considering the general Byzantine misbehaviour. It is shown that non-faulty nodes achieve consensus on K equilibria if there are K number of primary and secondary layers with non-faulty root nodes, each of which contains StrBYZ agents having at least one in-neighbor in the network. The analysis is extended to the case where the network has bounded uniform/non-uniform time delays on its communication links. The results are verified by numerical examples.