Event-triggered Privacy-Preserving Bipartite Consensus for Multi-Agent Systems Based on Encryption

In this paper, the privacy-preserving-based bipartite consensus control problem is investigated for a class of discrete-time nonlinear multi-agent systems (MASs). The classical bipartite consensus control implementation relies on the explicit information exchange between agents, which will lead to the possible leakage of agents’ private information, especially the initial states. Therefore, to prevent data disclosure to neighbors inside the MASs and the outside eavesdroppers, the data is encrypted by means of Paillier encryption scheme during information transmission. This means each agent first sends the relative data in the form of ciphertext to its neighbors for further encryption process, and then restores the control protocol based on the returned encrypted information from the neighbors. Since homomorphic encryption only works for integers, the data must be quantized before encryption, and it will inevitably result in the quantization error. On the other hand, for the purpose of saving communication resources, both decentralized and distributed event-triggered schemes are also proposed. Resorting to the Lyapunov stability theory and algebraic graph theory, sufficient conditions are derived ensuring that the MASs subject to a confidential communication agreement can achieve the bounded bipartite consensus. Two numerical examples are presented to verify the validity of the theoretical results.