Privacy-Preserving Average Consensus via Enhanced State Decomposition

In this paper, a new state decomposition method is proposed to achieve average consensus privately without any reliable neighbor node. This method, named as enhanced state decomposition method, can divide each node state into
$\vert N_{i}\vert+ 1 (\vert N_{i}\vert$
is the number of neighboring nodes) sub states to avoid disclosing the state information. Specifically,
$\vert N_{i}\vert$
decomposed states replace the initial state to participate in the calculation and interaction between nodes, while the other decomposed states only interact with the homologous nodes and are completely closed for other neighbor nodes. Every initial value of these sub states is randomly selected, but their average values are fixed on the values of the initial states, which plays a key role to ensure convergence to the expected consensus. Different from the original state decomposition method, enhanced decomposition method does not require the participation of a reliable neighbor. Numerical simulation shows the effectiveness of this method and is compared with other methods.