Differential Privacy for Second-Order Bipartite Consensus Over Signed Digraph

This article addresses the differential privacy problem for second-order multiagent systems (MASs) over signed digraph. To this end, both position and velocity states are disturbed by Laplacian noise. As for structurally balanced case, necessary and sufficient conditions for almost sure bipartite consensus are presented, upon which an
$\epsilon $
-differential privacy algorithm is designed. Along with the devised setup, the tradeoff between system performance and degree of privacy protection is discussed, and the optimal noise is elaborated as well. The proposed privacy preserving scheme is further extended to the case with structurally unbalanced graph, and criteria for almost sure stability or interval bipartite consensus are induced. Finally, numerical simulations and the application to power systems show the effectiveness of the theoretical findings as well as the developed privacy scheme.