Average Controllability of Complex Networks With Laplacian Dynamics
Jiawei Zhu, Linying Xiang, Yanying Yu, Fei Chen, Guanrong Chen · IEEE Transactions on Circuits and Systems I Regular Papers · 2021
The trace of the controllability Gramian quantifies the average controllability in all directions in the system state space. In this paper, we investigate the average controllability of a semistable networked system with Laplacian dynamics and derive upper and lower bounds on the trace of its pseudo-controllability Gramian matrix. We show that these bounds are solely determined by the network topology, which can be obtained without computing any higher-dimensional matrix. We find that a sparse or a scale-free network is easy to control in terms of the average controllability. We then investigate the effect of the edges with negative weights on the average controllability for a signed network with Laplacian dynamics. We find that a small number of negatively-weighted edges can significantly affect the average controllability of the signed network. We finally demonstrate that many real-world networks are easy to control via manipulating negatively-weighted edges.