This paper aims at secure and privacy-preserving consensus algorithms of networked systems. Due to the technical challenges behind decentralized design of such algorithms, the existing results are mainly restricted to a network of systems with simplest first-order dynamics. Like many other control problems, breakthrough of the gap between first-order dynamics and higher-order ones demands for more advanced technical developments. In this paper, we explore a Paillier encryption based average consensus algorithm for a network of systems with second-order dynamics, with randomness added to network weights. The conditions for privacy-preserving, especially depending on consensus rate, are thoroughly studied with theoretical analysis and numerical verification.

本文旨在研究网络系统的安全和隐私保护共识算法。由于这种算法的分散设计背后的技术挑战，现有结果主要限于具有最简单一阶动力学的系统网络。像许多其他控制问题一样，要突破一阶动力学与高阶动力学之间的鸿沟，就需要更先进的技术发展。在本文中，我们探索了一种基于Paillier加密的平均共识算法，该算法用于具有二阶动力学的系统网络，并且网络权重增加了随机性。通过理论分析和数值验证，充分研究了隐私保护的条件，特别是取决于共识率。