Toward robust network controllability: Insights and future directions

Network controllability refers to the ability of a networked system to drive its state to any desired configuration through control inputs. Controllability robustness ensures that this capability is maintained or retained under structural variations, such as node or edge failures caused by malicious attacks or random perturbations, which is critically important for real-world networks. This paper reviews existing metrics, evaluation methods and optimization strategies for controllability robustness, introducing also modeling techniques for attack processes. Analytical techniques, empirical simulations and machine learning-based approaches are presented, highlighting their respective advantages and limitations. Finally, some future directions are briefly discussed in four key areas: metrics design, evaluation refinement, optimization algorithms, and attack process modeling. By addressing these challenges, it is expected to develop more robust and stronger resilient networked systems.