Closed-Loop Control of Complex Networks: A Trade-Off between Time and Energy

Yong-Zheng Sun, Si-Yang Leng, Ying-Cheng Lai, Celso Grebogi, and Wei Lin

Phys. Rev. Lett. 119, 198301 – Published 7 November 2017

Abstract

Controlling complex nonlinear networks is largely an unsolved problem at the present. Existing works focus either on open-loop control strategies and their energy consumptions or on closed-loop control schemes with an infinite-time duration. We articulate a finite-time, closed-loop controller with an eye toward the physical and mathematical underpinnings of the trade-off between the control time and energy as well as their dependence on the network parameters and structure. The closed-loop controller is tested on a large number of real systems including stem cell differentiation, food webs, random ecosystems, and spiking neuronal networks. Our results represent a step forward in developing a rigorous and general framework to control nonlinear dynamical networks with a complex topology.

Received 27 April 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.198301

Physics Subject Headings (PhySH)

Dynamics of networks Network stability

Ecological networks Networks & random structures

Interdisciplinary PhysicsNonlinear DynamicsNetworks

Authors & Affiliations

Yong-Zheng Sun^1,2, Si-Yang Leng^1,3,4, Ying-Cheng Lai⁵, Celso Grebogi⁶, and Wei Lin^1,3,*

¹Center for Computational Systems Biology of ISTBI, Fudan University, Shanghai 200433, China
²School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
³School of Mathematical Sciences and LMNS, Fudan University, Shanghai 200433, China
⁴Collaborative Research Center for Innovative Mathematical Modelling, Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan
⁵School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287-5706, USA
⁶Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom