Control of Multiagent Networks With Misbehaving Nodes Over Directed Graph Topologies

In this article, we study multiagent networks over directed graph topologies involving nodes subject to exogenous disturbances (i.e., misbehaving nodes) and nodes that receive feedback control signals (i.e., driver nodes) for the purpose of suppressing the adverse effects of misbehaving nodes. The number of driver nodes can be less than the total number of nodes in the multiagent network. Specifically, we propose proportional–integral feedback controllers to be executed by driver nodes. These controllers guarantee the stability of the overall multiagent network in the sense of input-to-state stability (i.e., they make the resulting closed-loop system matrix Hurwitz). Furthermore, we utilize a graph-theoretical approach that allows users to find the steady-state values of critical nodes without requiring the knowledge of the Laplacian matrix of the overall multiagent network. The results presented in this article pave the way for understanding how driver nodes need to be selected to suppress the effect of misbehaving nodes on the neighborhood of critical nodes, which is further illustrated through illustrative numerical examples.