Bipartite Consensus in Multi-agent Systems: A Node Decomposition Approach for Privacy Preservation

The consensus control protocol of the cooperative-competitive network requires nodes to transmit their own information to the rival group, which is detrimental to the security of the information. In this paper, we propose a novel node decomposition mechanism, which can prevent the state information from being revealed during the information exchange for multi-agent systems with antagonistic interactions. For each node, one of the two subnodes takes over the role of the primitive node with cooperative neighbors, and the other one is involved in antagonistic interactions. Under this method, the connectivity and structurally balanced of the system are not changed, so it can still achieve bipartite consensus. Besides, although the initial values of the two subnodes are chosen randomly, the average of these subnodes corresponds to the original state value, ensuring precise bipartite consensus. Moreover, we also prove that the privacy of a node can be guaranteed if and only if it has a neighbor in the same group. The effectiveness of the proposed approach is demonstrated by a numerical example.