  Average consensus protocols emerge with a central role in distributed systems
and decision-making such as distributed information fusion, distributed
optimization, distributed estimation, and control. A key advantage of these
protocols is that agents exchange and reveal their state information only to
their neighbors. Yet, it can raise privacy concerns in situations where the
agents' states contain sensitive information. In this paper, we propose a novel
(noiseless) privacy preserving distributed algorithms for multi-agent systems
to reach an average consensus. The main idea of the algorithms is that each
agent runs a (small) network with a crafted structure and dynamics to form a
network of networks (i.e., the connection between the newly created networks
and their interconnections respecting the initial network connections).
Together with a re-weighting of the dynamic parameters dictating the
inter-agent dynamics and the initial states, we show that it is possible to
ensure that the value of each node converges to the consensus value of the
original network. Furthermore, we show that, under mild assumptions, it is
possible to craft the dynamics such that the design can be achieved in a
distributed fashion. Finally, we illustrate the proposed algorithm with
examples.
