Spectrum of controlling and observing complex networks

Gang Yan, Georgios Tsekenis, Baruch Barzel, Jean Jacques Slotine, Yang Yu Liu, Albert László Barabási

Research output: Contribution to journalArticlepeer-review

Abstract (may include machine translation)

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.

Original languageEnglish
Pages (from-to)779-786
Number of pages8
JournalNature Physics
Volume11
Issue number9
DOIs
StatePublished - 4 Sep 2015

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