Abstract
This paper studies the differential privacy-preserving problem for multi-agent systems (MASs) in the presence of antagonistic information over signed digraph. As for the structurally balanced case, an ε-differential privacy algorithm is proposed, upon which some sufficient conditions guaranteeing almost sure bipartite consensus are given. Based on the above scheme, the tradeoff between the system performance and the privacy guarantee is elaborated, and the optimal noise is also devised. Moreover, the proposed privacy preserving scheme is further applied to the scenario of structurally unbalanced graph, where a criterion with respect to almost sure stability of the considered system is derived, as well as the privacy preserving condition. This extends the balanced interaction scenario, and consequently the cooperative multi-agent systems. Finally, numerical simulations are presented to demonstrate the effectiveness of our results.
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