Investigating the energy cost for controlling complex social networks - Chen, Hong (Nanyang Technological University, 2021)
The controllability of complex networks has recently emerged as a promising field of interdisciplinary research. At its core, the idea is to study, given a dynamical system modeled by state equations with linear dynamics, whether or not the state vector of a complex system could be driven towards some predefined state. Different from traditional control engineering, which deals only with small dimensions, the controllability of complex networks borrows techniques from graph theory and statistical physics to guarantee the controllability of an arbitrary complex system with arbitrary dimensions. This thesis advances the field by exploring the controllability of such networked systems particularly in the context of social physics (socio-physics). There are three parts to the thesis. Firstly, an energy cost optimization problem is solved, where the choice of target nodes (which individuals) to control is being optimized. It was found that using the optimization algorithm, the energy cost is minimized when the target nodes are close to the driver nodes, leading to reduction in the control energy by a few orders of magnitude. Secondly, the scaling laws of the energy cost as a function of final control time Tf when controlling a complex social network with conformity behavior is presented. It was found that, when compared to networks without conformity, the mechanism of conformity always leads to a situation where the network is easier to control. Thirdly, how zealots, individuals with unwavering opinions, influence the amount of effort needed to control a complex social network is studied. It was found that the presence of zealots alters the energy cost at a quadratic rate with respect to their own fixed beliefs. However, whether or not the zealots’ presence increases or decreases the energy cost, relative to the situation where there were no zealots present, is affected by the interplay between different parameters such as the zealots’ beliefs, number of drivers, final control time regimes, network effects, network dynamics, number and configurations of normal nodes influenced by the zealots.