Resilience of Time-Varying Communication Graphs for Consensus of Changing Sets of Computing Agents

System performance of distributed control systems and networked computing systems is strongly dependent of the underlying communication topology. This paper considers the rarely studied problem of how the topology can maintain resilience by reconfiguration in case that agents leave or join the network during online operation. Existing optimization-based approaches which reconfigure the entire network can typically not be used in this case, since the computational burden for online application is too high. Thus, this paper proposes a novel combined offline-online scheme which optimizes the topology for high convergence rate (of e.g. consensus problems) while providing guarantees for the robustness against agent failures. In the offline part, an optimization of the entire topology is carried out using novel constraints to prepare resilience of the online procedure. For the latter, the proposed scheme guarantees that robustness is maintained for joining agents and if a specified number of agents leave the network. In simulation, the proposed scheme is compared to existing approaches and the advantages of the online-offline procedure are demonstrated.