Privacy-Preserved Consensus Control for Second-Order Multiagent Systems: a Position and Velocity Simultaneous Perturbation Approach

In this article, we consider the problem of privacy preservation in consensus control for second-order integrator multiagent systems (MASs). Specifically, we consider the setting where the initial position and velocity of each legitimate agent are both private, an internal or external adversary wants to identify them based on the information it obtains. To deal with this scenario, we propose a privacy preservation algorithm based on a position and velocity simultaneous perturbation technique. To be specific, our algorithm consists of a collaborative scrambling phase and a convergence phase. In the scrambling phase, each agent is required to produce two sets of edge-based perturbation signals that are, respectively, imposed on the local position and velocity signals before transmission, with the purpose of preserving privacy; in the convergence phase, each agent updates its state per a normal rule, aiming to achieving accurate consensus. Also, we establish a system-theoretic framework to analyze privacy performance by examining the indistinguishability of private values’ arbitrary variations to adversaries, and further show that, an internal adversary cannot infer the privacy of a legitimate agent provided it has at least one legitimate in-neighbor or out-neighbor, and the privacy is leaked out once that agent exclusively connects to the internal adversary in bidirectional way. As for external eavesdroppers, they can never infer any agent’s privacy if the gain parameters in the scrambling phase are not accessible to them. Finally, two simulation examples illustrate the validity of the proposed approach.