A new focus in the science of networks: towards methods for design

Abstract

In recent years, a realization that networks are ubiquitous in the natural and engineered worlds has led to a burgeoning interest in finding commonalities in their structures and dynamics. Here, we introduce a new design focus in this science of networks by proposing generic methods for synthesizing network controllers that exploit the topological structure . That is, we motivate a canonical controller synthesis problem for networks that has applications in such diverse areas as virus-spreading control and air traffic flow management. We address this design problem by using new techniques from decentralized control theory . Specifically, we mesh optimization machinery together with eigenvalue sensitivity and graph theory notions to identify general structural features of optimally actuated networks. From these features, we are in turn able to explicitly construct high-performance controllers, i.e. the ones that best exploit the network's topological structure. Our general approach for controller design is important because it both provides a broad insight into the structure of well-designed networks and contributes engineering solutions in numerous application areas (e.g. reduction in management delays and human-controller workload in air traffic systems).