Energy-Aware Controllability of Complex Networks

Understanding the fundamental principles and limitations of controlling complex networks is of paramount importance across natural, social, and engineering sciences. The classic notion of controllability does not capture the effort needed to control dynamical networks, and quantitative measures of controllability have been proposed to remedy this problem. This article presents an introductory overview of the practical (i.e., energy-related) aspects of controlling networks governed by linear dynamics. First, we introduce a class of energy-aware controllability metrics and discuss their properties. Then, we establish bounds on these metrics, which allow us to understand how the structure of the network impacts the control energy. Finally, we examine the problem of optimally selecting a set of control nodes so as to minimize the control effort, and compare the performance of some simple strategies to approximately solve this problem. Throughout the article, we include examples of structured and random networks to illustrate our results.