Group consensus of multi-agent systems with additive noises

This paper is concerned with group consensus of multi-agent systems (MASs) that consist of two groups in additive noise environments. First, a control protocol is proposed based on the state information of each agent’s neighbors corrupted by additive noises. Second, some sufficient conditions and necessary conditions are obtained for the following two types of group consensus behaviors. (1) Pure group consensus: agents in both groups have the same behavior (weak consensus or strong consensus); (2) hybrid group consensus: agents in different groups achieve different consensus behaviors. It is revealed that the influence between the two groups should be attenuated such that the MASs can achieve group consensus in additive noise environments, i.e., the affected group must fight against the influence that comes from another group. Finally, some simulation examples are given to illustrate the feasibility of the theoretical results.