Minimizing Worst-Case Cyber Graph Reconfigurations in Resilient Cyber-Physical Systems

This letter addresses the resilience of cyber-physical systems with fixed connectivity of the physical network and controllable connectivity of the cyber network. We focus on the case where, to ensure effective control, the connected components of both networks should always align. In other words, when some of the physical lines fail, the cyber graph should be reconfigured via link additions or removals. Such a need arises, e.g., in the distributed control of power grids. To ensure the resilience of the system to major disruptions, we aim to design a cyber network that minimizes the number of cyber reconfigurations in the worst case of physical failure. We will call this number incongruity. Our contributions are threefold: (1) an analytical formula for computing incongruity, (2) a proof that an optimally resilient cyber graph can always be found in the form of a tree, and (3) a bi-level MILP formulation of the problem derived from our theoretical results. The latter contribution is of particular importance given the existence of solvers for bi-level MILPs and the fact that the straightforward MILP formulation of the problem would be tri-level.