TY - JOUR
T1 - Spectrum of controlling and observing complex networks
AU - Yan, Gang
AU - Tsekenis, Georgios
AU - Barzel, Baruch
AU - Slotine, Jean Jacques
AU - Liu, Yang Yu
AU - Barabási, Albert László
N1 - Publisher Copyright:
© 2015 Macmillan Publishers Limited. All rights reserved.
PY - 2015/9/4
Y1 - 2015/9/4
N2 - Recent studies have made important advances in identifying sensor or driver nodes, through which we can observe or control a complex system. But the observational uncertainty induced by measurement noise and the energy required for control continue to be significant challenges in practical applications. Here we show that the variability of control energy and observational uncertainty for different directions of the state space depend strongly on the number of driver nodes. In particular, we find that if all nodes are directly driven, control is energetically feasible, as the maximum energy increases sublinearly with the system size. If, however, we aim to control a system through a single node, control in some directions is energetically prohibitive, increasing exponentially with the system size. For the cases in between, the maximum energy decays exponentially when the number of driver nodes increases. We validate our findings in several model and real networks, arriving at a series of fundamental laws to describe the control energy that together deepen our understanding of complex systems.
AB - Recent studies have made important advances in identifying sensor or driver nodes, through which we can observe or control a complex system. But the observational uncertainty induced by measurement noise and the energy required for control continue to be significant challenges in practical applications. Here we show that the variability of control energy and observational uncertainty for different directions of the state space depend strongly on the number of driver nodes. In particular, we find that if all nodes are directly driven, control is energetically feasible, as the maximum energy increases sublinearly with the system size. If, however, we aim to control a system through a single node, control in some directions is energetically prohibitive, increasing exponentially with the system size. For the cases in between, the maximum energy decays exponentially when the number of driver nodes increases. We validate our findings in several model and real networks, arriving at a series of fundamental laws to describe the control energy that together deepen our understanding of complex systems.
UR - http://www.scopus.com/inward/record.url?scp=84940795604&partnerID=8YFLogxK
U2 - 10.1038/nphys3422
DO - 10.1038/nphys3422
M3 - Article
AN - SCOPUS:84940795604
SN - 1745-2473
VL - 11
SP - 779
EP - 786
JO - Nature Physics
JF - Nature Physics
IS - 9
ER -