Optimal distributed consensus on unknown undirected graphs

For multi-agent networks described by fixed undirected connectivity graphs, the problem of optimal controller synthesis for distributed consensus is addressed without assuming prior knowledge about the global network topology. Under the proposed control scheme, the agents maintain a Nash equilibrium by updating their beliefs about the network topology over time and by computing their decisions via online optimization. This equilibrium attains finite-time consensus in minimum time while optimizing a quadratic transient performance index on the way to consensus.