Privacy-preserving average consensus for second-order discrete-time multi-agent systems

This study addresses the privacy-preserving average consensus problem in second-order discrete multi-agent systems under strongly connected and balanced graphs. When both velocity and position states of each agent are measurable, a novel lightweight algorithm is proposed by introducing perturbation signals into the transmitted information. Specifically, the algorithm is divided into two stages. In the initial stage, each agent introduces perturbation signals into its initial position and velocity states during transmission to confound potential attackers. In the subsequent stage, the agents use a standard average consensus algorithm to update their states, ensuring accurate convergence to the average of the initial states. Additionally, further considering the scenario where the velocity state is unavailable for each agent, an improved edge-based perturbation algorithm is introduced. Both algorithms not only effectively prevent the internal honest-but-curious agents from accurately inferring the initial states of other agents, except in the specific case where the curious agent is the sole neighbor of the target agent, but also protect privacy from the external eavesdroppers. Lastly, several numerical examples are conducted to validate the effectiveness of the proposed theoretical approaches.