Controlling complex networks with complex nodes

Modern society relies on many interdependent networks such as electric grids, supply chain networks and ecological networks. This Perspective describes progress and challenges in harnessing insights from statistical physics and control theory to develop better control and management strategies of such complex networks and infrastructure systems. Real-world networks often consist of millions of heterogenous elements that interact at multiple timescales and length scales. The fields of statistical physics and control theory both contribute different perspectives for understanding, modelling and controlling these systems. To address real-world systems, more interaction between these fields and integration of new paradigms such as heterogeneity and multiple levels of representation will be necessary. It may be possible to expand models from statistical physics to integrate the notion of feedback (both positive and negative) and to extend control theory formulations to more mesoscopic analysis over averages of collections of degrees of freedom. There is also the need to integrate theoretical models, machine learning and data-driven control methods. We review recent progress and identify opportunities to help advance understanding and control of real-world systems from oscillator networks and social networks to biological and technological networks.