Multi-round Attacks on Structural Controllability Properties for Non-complete Random Graphs

The notion of controllability, informally the ability to force a system into a desired state in a finite time or number of steps, is most closely associated with control systems such as those used to maintain power networks and other critical infrastructures, but has wider relevance in distributed systems. It is clearly highly desirable to understand under which conditions attackers may be able to disrupt legitimate control, or to force overriding controllability themselves. Following recent results by Liu et al., there has been considerable interest also in graph-theoretical interpretation of Kalman controllability originally introduced by Lin, structural controllability. This permits the identification of sets of driver nodes with the desired state-forcing property, but determining such nodes is a W[2]-hard problem. To extract these nodes and represent the control relation, here we apply the Power Dominating Set problem and investigate the effects of targeted iterative multiple-vertex removal. We report the impact that different attack strategies with multiple edge and vertex removal will have, based on underlying non-complete graphs, with an emphasis on power-law random graphs with different degree sequences.