A temporal segmentation algorithm for restoring the controllability of networked control systems

Restoring the controllability of networked control systems is a fundamental issue that needs to be settled, especially when malicious attacks or malfunctions occur. Previous studies tried to address such an issue by adding extra driver nodes or rewiring edges, which will inevitably change the original network structure. In this paper, an algorithm to restore the controllability of networked systems while preserving the integrity of the original network structure is proposed. Specifically, a static uncontrollable network will be transformed into a controllable temporal network by means of the cactus-based segmentation method. The original problem will be equivalent to the classical set cover problem, which is known to be NP-Hard, if the least number of segmentations is considered. An approximation algorithm with polynomial time complexity is proposed and it is proved that the solution to the problem is two-optimal. Finally, simulations are carried out to verify the effectiveness and feasibility of the proposed algorithm.