Finite-time information consensus for multi-agent systems with fixed and switching topologies

In this paper, we study the consensus problems for a group of interacting agents. First, we analytically establish the explicit expression of the consensus state for the entire group. Second, we prove that the agents of the group under a particular type of nonlinear interaction can reach the consensus state in finite time in the scenarios with fixed and switching undirected topologies. The results are also extended to the case where the topology of the group is directed and satisfies a detailed balance condition on coupling weights. Third, some numerical examples are provided to analyze the influencing factors of the convergence time, that is, the parameter of the particular interaction function and the algebraic connectivity of graphs. Finally, an application of the theoretical results in sensor networks is given, namely, computing the maximum-likelihood estimate of unknown parameters.