Finite-time consensus for multi-agent systems with application to sensor fusion

This paper studies the finite-time consensus for a group of dynamic agents. For the entire group, we establish the explicit expression of the consensus state, which can be characterized by the new concept of weighted average consensus with respect to a monotonic function. For networks with undirected topology, we prove that the weighted average consensus with respect to a monotonic function can be solved in finite time when the interactions among agents are taken as power-law based function. These results are further extended to a class of networks where the topologies are directed and satisfy a detailed balance condition on coupling weights. As an application of the theoretical results to sensor fusion, we propose a distributed scheme to compute the maximum-likelihood (ML) estimate of unknown parameters. Numerical simulations show that the distributed scheme can be used to compute the ML estimate of unknown parameters effectively.