Finite-time Consensus in the Presence of Malicious Agents

A finite-time consensus protocol is developed for a connected network of agents, where communication between agents occurs locally, some of the agents are malicious, and the non-malicious or cooperative agents do not know the identities of the malicious ones. The agents are modeled with first-order dynamics, and the inputs to each agent that enable consensus are designed using the principles of sliding mode control (SMC). The use of the SMC algorithm guarantees finite-time consensus and ensures that in the transient stage, the agents' states are contained within the convex hull formed by their initial conditions (ICs). With this feature and by modeling the network as a connected graph, the protocol guarantees consensus amongst the cooperative agents when the malicious agents transmit values of their states lying outside the convex hull of ICs, and the graph formed by the cooperative agents with the removal of the malicious agents is strongly connected. The protocol does not require a cooperative agent to know the number of malicious or other cooperative agents in the network, and is based only on local communication.