Optimal Distributed Finite-Time Consensus On Unknown Undirected Graphs

For multiagent networks described by undirected connectivity graphs, the problem of optimal distributed consensus without prior knowledge of global connectivity is considered. The problem is formulated as a decentralized linear quadratic game, and a linear dynamic feedback scheme that couples the tasks of learning the network topology and driving the network state is shown to solve the game and achieve a Nash equilibrium. This solution results in finite-time consensus in minimum time, and optimizes the transient behavior on the way to consensus with respect to a quadratic global performance measure.