Trade-offs between driving nodes and time-to-control in complex networks

Abstract

Recent advances in control theory provide us with efficient tools to determine the minimum number of driving (or driven) nodes to steer a complex network towards a desired state. Furthermore, we often need to do it within a given time window, so it is of practical importance to understand the trade-offs between the minimum number of driving/driven nodes and the minimum time required to reach a desired state. Therefore, we introduce the notion of actuation spectrum to capture such trade-offs, which we used to find that in many complex networks only a small fraction of driving (or driven) nodes is required to steer the network to a desired state within a relatively small time window. Furthermore, our empirical studies reveal that, even though synthetic network models are designed to present structural properties similar to those observed in real networks, their actuation spectra can be dramatically different. Thus, it supports the need to develop new synthetic network models able to replicate controllability properties of real-world networks.

Correlations in the degeneracy of structurally controllable topologies for networks

“…In addition, we note that the diverse selection of empirical networks evaluated in this study offers insight into network structures that are independent of context. While this follows related work and avoids sample bias that arises when considering traditional generative models232633, taking a similar approach as this study, but focused upon a particular empirical context (e.g., cellular signaling networks, ecological networks) may offer network-specific insight.…”

On Node Controllability and Observability in Complex Dynamical Networks

“…• the state of the nodes associated to the columns of the matrix in eq. (19) corresponding to the block (R 22 ) −1 can be arbitrarily selected;…”

“…The first one is to establish in which nodes the control signals have to be injected. In the literature this is often referred to as the driver nodes selection problem [8,16,17,18,19,20]. The second problem is, obviously, the selection of the nodes that can be sensorized in order to get the measurements needed for the observation of the state of others nodes and for the synthesis of the control action.…”

Identifying and using driver nodes in temporal networks

“…We can utilize these changes in network's wiring to increase efficiency of control in terms of the time and energy required to gain control compared to the static networks [16]. Also, including time in the definition of controllability allows to explicitly study the time necessary to gain control; in contrast, this is an area that only receives implicit treatment in static networks [31]. These motivate the need to study the controllability of temporal networks.…”