Structural Control of Drift-free Bilinear Systems under Link Failures and Sparsity Constraints

We study structural controllability properties of drift-free bilinear systems under link failures using a graph theoretic approach. We give an equivalent condition for structural controllability in the presence of link failures, which can be checked in polynomial time. We show that the problem of finding a sparsest structure for structural controllability under link failures is equivalent to a known NP-hard problem. We also consider the case of probabilistic link failures. The problem of deciding whether the underlying system is structurally controllable with a certain probability is equivalent to an NP-hard network reliability problem. Finally, we observe that the problem of designing a structurally controllable bilinear system from an uncontrollable one under nonuniform cost constraints is equivalent to an NP-complete strong connectivity augmentation problem.