Spectrum of controlling and observing complex networks

G. Yan, G. Tsekenis, B. Barzel, J.-J. Slotine, Y.-Y. Liu, A.-L. Barabási
Nature Physics
1-8 (2015).
August 10, 2015

Abstract

Observing and  controlling complex networks are of paramount interest for understanding  complex physical, biological and technological systems. Recent studies have  made important advances in identifying sensor or driver nodes, through which  we can observe or control a complex system. Yet, 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 to a series of fundamental laws to describe the control energy that  together deepen our understanding of complex systems.

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