Comprehensively Privacy-Preserving Consensus of General Linear Multiagent Systems: an Isomorphism Transformation Approach

In this note, we consider the problem of privacy preservation in consensus for general linear multiagent systems (MASs), where the system matrices, input and state trajectories are all private information, and required to comprehensively preserve against honest-but-curious adversaries. To mitigate this problem, a novel isomorphism transformation approach is proposed in this note. Specifically, we first use an encoding isomorphism to map actual, confidential agents to virtual, isomorphic agents, and then design the distributed protocol over a network that characterizes the interactions among isomorphic agents, to steer them toward consensus. Finally, by virtue of decoding isomorphism, we retrieve the local protocol for each actual agent, which enables the actual agents to achieve consensus. By virtue of group theory, we quantify the amount of guaranteed privacy, and further discuss how much privacy is compromised for four specific scenarios where the adversary has acquired partial side information. As a by-product, several specific isomorphisms are given, which not only can protect privacy, but have definite geometric meanings. Furthermore, the distinctive advantages of the proposed approach are expounded in details. The theoretical results are illustrated via two examples.