Privacy Preserving-Based Resilient Consensus for Multiagent Systems Via State Decomposition

This article addresses privacy preserving-based resilient consensus for discrete-time multiagent systems, where some adversarial agents try to steal private information and break the consensus property of the system. First, an attack model with the worst-case malicious behaviors is employed to simulate the adversarial environment, which can remove some general constraints about attackers. Then, a novel state decomposition mean-subsequence-reduce algorithm is proposed, which cannot only ensure the accurate consensus but also exhibit a high level of privacy preservation for initial states and the strong resilience to adversaries. Second, a series of different decomposition functions is used to decompose the initial state of each agent into two substates, and different linear integration functions are also adopted to combine two substates into original states. Moreover, the different weights of two substates are employed to describe the interaction. Third, a step-size sequence is introduced to realize the resilient consensus and to generate greater uncertainty. It is proven that the privacy of the initial states can be preserved even if all neighbors of one regular agent are compromised to adversarial agents. Furthermore, a sufficient and necessary condition, associated with the time-varying directed network, is obtained to realize resilient consensus. Finally, a simulation example is presented to validate the proposed results.