Network topology identification under the multi-agent agreement protocol

This paper investigates the problem of identifying the interaction geometry of a set of agents, whose collective goal are to achieve consensus under an agreement protocol. By classifying agents into different subsets based on their behavior, as well as introducing the so-called input and output agents, a relationship between the transfer function matrix and the identifiability of system parameters is established. Specifically, two cases are considered. If the set of input agents coincides with the set of output agents, the number of edges in the input agent set, in the complement of input agent set, and between these two sets can be uniquely identified. Thus, the search space of feasible graphs becomes much smaller. The problem can be solved in polynomial time, and an algorithm is provided. Moreover, if all the agents in the system are output agents, parameters of the system can be uniquely identified, and an algebraic method is given to exactly recover the graph topology. A numerical example illustrates the effectiveness of the proposed algorithm.