Privacy-preserving Resilient Consensus for Multi-agent Systems in a General Topology Structure

Recent advances of consensus control have made it significant in multi-agent systems such as in distributed machine learning, distributed multi-vehicle cooperative systems. However, during its application it is crucial to achieve resilience and privacy; specifically, when there are adversary/faulty nodes in a general topology structure, normal agents can also reach consensus while keeping their actual states unobserved. In this article, we modify the state-of-the-art Q-consensus algorithm by introducing predefined noise or well-designed cryptography to guarantee the privacy of each agent state. In the former case, we add specified noise on agent state before it is transmitted to the neighbors and then gradually decrease the value of noise so the exact agent state cannot be evaluated. In the latter one, the Paillier cryptosystem is applied for reconstructing reward function in two consecutive interactions between each pair of neighboring agents. Therefore, multi-agent privacy-preserving resilient consensus (MAPPRC) can be achieved in a general topology structure. Moreover, in the modified version, we reconstruct reward function and credibility function so both convergence rate and stability of the system are improved. The simulation results indicate the algorithms’ tolerance for constant and/or persistent faulty agents as well as their protection of privacy. Compared with the previous studies that consider both resilience and privacy-preserving requirements, the proposed algorithms in this article greatly relax the topological conditions. At the end of the article, to verify the effectiveness of the proposed algorithms, we conduct two sets of experiments, i.e., a smart-car hardware platform consisting of four vehicles and a distributed machine learning platform containing 10 workers and a server.