Robust design of cooperative systems against attacks

While the use of a communication network facilitates the development of cooperative control for networked systems, it comes at a price that the systems become vulnerable to data attacks by an adversary. In this paper, we consider consensus dynamics on networked systems with strongly connected directed graphs in the presence of an additive stealthy attacker. The attacker has a linear dynamics and can corrupt the local state feedback of the system´s agents by interconnecting with their communication network and inserting external attacks (or injections) with the intent of destabilizing the consensus dynamics. In order to make the consensus dynamics robust against such attacks, a hidden network, interconnected with the original consensus network, is introduced. The hidden network is designed to maintain stability of the overall system by competitively interacting with the original consensus network but without requiring any information about the adversary. Lyapunov analysis and design methods are presented which provide an explicit rule on how to interconnect both networks. Furthermore, using the same analysis and design framework we show that the nodes that are being attacked can also be identified in a distributed manner. An example, which includes several scenarios, is used to illustrate the results.