A geometrical approach to control and controllability of nonlinear dynamical networks

Le-Zhi Wang, Ri-Qi Su, Zi-Gang Huang, Xiao Wang, Wen-Xu Wang, Celso Grebogi and Ying-Cheng Lai ()
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Le-Zhi Wang: School of Electrical, Computer and Energy Engineering, Arizona State University
Ri-Qi Su: School of Electrical, Computer and Energy Engineering, Arizona State University
Zi-Gang Huang: School of Electrical, Computer and Energy Engineering, Arizona State University
Xiao Wang: School of Biological and Health Systems Engineering, Arizona State University
Wen-Xu Wang: School of Electrical, Computer and Energy Engineering, Arizona State University
Celso Grebogi: Institute for Complex Systems and Mathematical Biology, King’s College, Meston Walk, University of Aberdeen
Ying-Cheng Lai: School of Electrical, Computer and Energy Engineering, Arizona State University

Nature Communications, 2016, vol. 7, issue 1, 1-11

Abstract: Abstract In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains an outstanding problem. Here we develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically meaningful, we consider restricted parameter perturbation by imposing two constraints: it must be experimentally realizable and applied only temporarily. We introduce the concept of attractor network, which allows us to formulate a quantifiable controllability framework for nonlinear dynamical networks: a network is more controllable if the attractor network is more strongly connected. We test our control framework using examples from various models of experimental gene regulatory networks and demonstrate the beneficial role of noise in facilitating control.

Date: 2016
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DOI: 10.1038/ncomms11323

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