Control of Multiagent Networks in the Presence of Misbehaving Nodes without the Knowledge of Global Network Objective ⋆

We focus on multiagent networks composed of single-integrator dynamics over a fixed, connected, and undirected graph. In the presence of misbehaving nodes, we propose a control architecture to suppress the adverse effects of misbehaving nodes on the rest of the network. In particular, we apply our control architecture to the control nodes, which utilize their own state information together with their assigned auxiliary sensing nodes’ state information. For maintaining the privacy of the global network objective (i.e., the synchronization command), neither the control nodes nor the auxiliary sensing nodes need not to be selected as leader node(s) (i.e., only leader node(s) know the global network objective and they are not a part of the proposed control architecture). Stability and convergence properties of the resulting closed-loop multiagent network are rigorously analyzed, where we reveal how the control nodes and the auxiliary sensing nodes need to be selected for suppressing the effect of misbehaving nodes in certain portions of the multiagent network such that the nodes in this portion perform the given global objective (i.e., approach to the synchronization command of the leader node). Finally, illustrative numerical examples are presented to show the efficacy of our proposed approach.