On optimal link removals for controllability degradation in dynamical networks

We consider the problem of controllability degradation in dynamical networks subjected to malicious attacks. Attacks on the networks are assumed to be in the form of the removal of interconnection links. We formulate an optimization problem that seeks sets of links whose removal causes maximal degradation in the rank of the controllability gramian. We apply the alternating direction method of multipliers and sequential convex programming to find local solutions to this combinatorial optimization problem. We provide illustrative examples to demonstrate the utility of our results.