Game Theoretical Designs of Resilient Cooperative Systems

In this paper, we consider the problem of designing a resilient cooperative system from the perspective of differential game theory, as the conflict between a defender (i.e., the system's control designer) and any potential attacker. Intuitively, a resilient system is one in which the defender is a superior player to any potential adversary. It is shown that, for cooperative networked systems that have a multi-layer information structure, the defender is superior to the attacker if the defender has a superior information structure in that it has access to more layers of information than those accessible to the attacker. This insight reveals that the networked consensus dynamics can be made resilient against attacks by introducing a hidden-layer network interconnected to the original consensus network but shielded from the attacker. Nash equilibrium and Lyapunov analysis are used to demonstrate resilience under all adversary strategies. Several scenarios are used to illustrate the proposed concepts and designs.