Resilient First-Order Consensus and Weakly Stable, Higher Order Synchronization of Continuous-Time Networked Multiagent Systems

Local interaction rules for consensus and synchronization are vital for many applications in distributed control of cyber-physical systems. However, most research in this area assumes all nodes (or agents) in the networked system cooperate. This paper considers local interaction rules for resilient first-order consensus and weakly stable, higher order synchronization whenever some of the agents in the network are Byzantine-like adversaries defined in a continuous-time setting. The normal agents have identical dynamics modeled by continuous-time, linear, time-invariant, weakly stable systems. Agents in the networked system influence one another by sharing state or output information according to a directed, time-varying graph. We present a resilient consensus protocol as well as dynamic state and output feedback control laws for the normal agents, to achieve the resilient consensus and synchronization objectives, respectively. We characterize the required network topologies using the property of network robustness. We demonstrate the results in simulation examples to illustrate the resilient synchronization output feedback control law.