Privacy preserving resilient consensus for delayed multi-agent systems: A scheme via trusted nodes

Abstract

This paper proposes a novel scheme for privacy preserving resilient consensus problem of multi-agent systems (MASs) by employing a set of trusted nodes with improved security against attacks, taking the bounded non-uniform time-varying communication delays into account. In the existence of faulty agents, the robustness of the underlying network is imperative. Enhancing network robustness often involves deploying redundant nodes and communication links, which, however, may incur high connectivity constraints and significant costs. We provide a solution for sparse networks by protecting a limited subset of nodes, called trusted nodes, from failures and attacks all the time. We propose a novel state decomposition MSR (SD-MSR) algorithm with trusted nodes. Any desired level of robustness can be achieved by regulating the quantity and location of trusted nodes. Additionally, a sufficient and necessary condition for achieving resilient consensus, and a high level of privacy protection of normal agents’ initial states is obtained. Finally, numerical simulation and the application to smart grids are provided to demonstrate the effectiveness of the proposed results.