Resilient Structural Sparsity in the Design of Consensus Networks

The consensus problem is relevant to different areas ranging from biology, social psychology, and physics to power systems and robotics. Two crucial aspects of the design of a consensus system are the implementation issues that arise in densely connected networks and the presence of malicious agents that try to cause a deviation from a synchronization state. In this article, we introduce a formulation to design the topology of a consensus network to improve its resilience to attacks while remaining sparse and consistent with the a priori structural relations between the agents. Through mathematical analysis and simulations on artificial and real-world cases, we show the benefits and usefulness of using this strategy to design resilient and structurally sparse consensus networks.