Finite-time consensus for leader-follower and leaderless swarms in the presence of malicious agents

A finite-time resilient consensus protocol (RCP) is developed for a connected network of agents, where communication between agents occurs locally, a few of the agents are malicious (MA), and the non-malicious or cooperating (CO) agents do not know the locations of the MA ones. Networks with a single leader and several followers as well as leaderless networks are considered. Agents are modelled with first-order dynamics, and the inputs to each CO agent that enable consensus are designed using the principles of sliding mode control (SMC). An SMC-based consensus protocol (CP), derived using the Laplacian matrix of the graph describing the network that permits consensus amongst CO agents, is first illustrated; that MA agents can prevent consensus with the use of this CP is also discussed. The SMC-based RCP proposed in this paper requires that the CO agents know the bounds, defined by a statistical distribution, of other CO agents, and that the subgraph of the CO agents be connected; knowledge of MA agents is not needed. With these assumptions, in the case of networks with a single MA agent, CO agents can reach a consensus by disregarding information transmitted by this agent if its state violates some statistical properties. On the other hand, multiple MA agents can be disregarded without the need for these assumptions, owing to the relations that hold with the occurrence of sliding mode. The RCP consists of a message-passing algorithm whose basis can be found in the distributed computing literature. The proposed RCP can also be applied for a leader-follower network.