Fast Restoring the Controllability of Networked Systems With Symmetric Weights

Structural controllability theory enables us to attain controllability of networked systems independent of edge weights. However, the theory is restricted to a strong assumption that all edge weights are independent of each other, limiting the practical application in most real life scenarios. In this paper, we develop a new theory to restore the controllability of networked systems with coupled edge weights, i.e., symmetric edge weights. Firstly, we show that an uncontrollable symmetric networked system can be transformed into a controllable temporal network by the sym-cactus-based segmentation method and provide the rigorous theoretical proof. Then we consider the least number of segmentation to restore the controllability as quickly as possible and reduce the problem to the classical set coverage problem. Finally, an approximate polynomial-time algorithm and a simulation example are provided to demonstrate the validity of our method.