  Distributed algorithms for multi-agent resource allocation can provide
privacy and scalability over centralized algorithms in many cyber-physical
systems. However, the distributed nature of these algorithms can render these
systems vulnerable to man-in-the-middle attacks that can lead to
non-convergence and infeasibility of resource allocation schemes. In this
paper, we propose attack-resilient distributed algorithms based on primal-dual
optimization when Byzantine attackers are present in the system. In particular,
we design attack-resilient primal-dual algorithms for static and dynamic
impersonation attacks by means of robust statistics. For static impersonation
attacks, we formulate a robustified optimization model and show that our
algorithm guarantees convergence to a neighborhood of the optimal solution of
the robustified problem. On the other hand, a robust optimization model is not
required for the dynamic impersonation attack scenario and we are able to
design an algorithm that is shown to converge to a near-optimal solution of the
original problem. We analyze the performances of our algorithms through both
theoretical and computational studies.
