Distributed Multi-agent Consensus with Multiple Group Information

This paper studies the discrete-time system for multi-agent consensus problem via group information. In this scheme, neither the absolute states nor inter-agent relative states are available. We partition a group of agents into several subgroups in probability, and then use the relative group information to update each agent state. In this paper, we focus on the group information as the average value of the states of agents in the corresponding subgroup. It is shown that when the agents are divided into only two subgroups, almost surely consensus is achieved if and only if the weighting parameter is greater than one. While the subgroup number m = 3 is considered, one more condition that the partition probability to the chosen two subgroups should he equal is required to guarantee the convergence. Numerical simulations are provided to demonstrate the validity of our results.