Distributed fault-tolerant consensus control for multi-agent systems with an event-triggered differential privacy strategy

This study investigates the problem of privacy-preserving fault-tolerant consensus control (FTCC) for discrete-time linear multivariate multi-agent systems (MASs) affected by actuator loss-of-effectiveness (LoE) faults and eavesdropping threats.To tackle this issue, two novel distributed FTCC schemes incorporating an eventtriggered differential privacy strategy (ETDPS) are proposed, wherein the ETDPS first perturbs the state of each agent by injecting random noise and subsequently determines whether to transmit the perturbed state based on an event-triggering condition with a state-independent triggering threshold.This strategy is designed to prevent the disclosure of initial states of agents to potential eavesdroppers while reducing the communication overhead induced by continuous transmissions.Building upon the ETDPS, two fault-tolerant consensus controllers are developed in a distributed manner, both of which guarantee consensus despite the presence of actuator degradation.The privacy level of the first controller is intrinsically determined by the system dynamics, whereas the second further enhances privacy by embedding a noise feedback mechanism (NFM) into the control protocol.Sufficient conditions are derived to achieve mean-square consensus and -differential privacy via matrix norm analysis.Simulation results validate the feasibility of the proposed ETDPS-based FTCC schemes.