Time Parameters Shape the Controllability of Temporally Switching Networks
Baoyu Hou · IEEE Transactions on Automatic Control · 2022
Based on temporally switching networks, this article studies the qualitative and quantitative influences of time parameters on network controllability. In particular, this article presents a necessary and sufficient condition under which the network controllability must take into account time parameters. For the time parameters that never participate in determining network controllability, a more concise expression of controllability criterion is derived. From the perspective of input matrix formulation, this article also presents a sufficient condition under which the network controllability could avoid the interference of time parameters. By taking control energy as the quantitative measurement, it is difficult to give a general conclusion on whether the increase in time parameters is beneficial or detrimental to network controllability. Because the increase in time parameter$T_{i}$($i \in \lbrace 1,2,\ldots,m\rbrace$) would decrease the lower bound of minimum control energy. However, the increase in time parameter$T_{i}$($i \in \lbrace 2,3,\ldots,m-1\rbrace$) may cause an upsurge in the upper bound of minimum control energy. In addition, we find that different time parameters ($T_{i}$and$T_{j}$,$i e j$) usually have different importance to the control energy. Through simulations based on real-world temporal network data, we show that there exists a statistically significant correlation between time parameter influence level and network characteristic. This article highlights for the first time that subtle changes in time parameters could reshape or even worsen the controllability of temporally switching networks.