title: Energy scaling and reduction in controlling complex networks.
abstract: Recent works revealed that the energy required to control a complex network depends on the number of driving signals and the energy distribution follows an algebraic scaling law. If one implements control using a small number of drivers, e.g. as determined by the structural controllability theory, there is a high probability that the energy will diverge. We develop a physical theory to explain the scaling behaviour through identification of the fundamental structural elements, the longest control chains (LCCs), that dominate the control energy. Based on the LCCs, we articulate a strategy to drastically reduce the control energy (e.g. in a large number of real-world networks). Owing to their structural nature, the LCCs may shed light on energy issues associated with control of nonlinear dynamical networks.
authors.affiliation: School of Electrical, Computer, and Energy Engineering, Arizona State University , Tempe, AZ 85287, USA.
authors.forename: Yu-Zhong
authors.initials: YZ
authors.lastname: Chen
authors.affiliation: School of Electrical, Computer, and Energy Engineering, Arizona State University , Tempe, AZ 85287, USA.
authors.forename: Le-Zhi
authors.initials: LZ
authors.lastname: Wang
authors.affiliation: Department of Systems Science , School of Management and Center for Complexity Research, Beijing Normal University , Beijing 100875, People's Republic of China.
authors.forename: Wen-Xu
authors.initials: WX
authors.lastname: Wang
authors.affiliation: School of Electrical, Computer, and Energy Engineering, Arizona State University , Tempe, AZ 85287, USA.
authors.forename: Ying-Cheng
authors.initials: YC
authors.lastname: Lai
keywords: complex networks; control; scaling law