Global network control from local information

In the classical control of network systems, the control actions on a node are determined as a function of the states of all nodes in the network. Motivated by applications where the global state cannot be reconstructed in real time due to limitations in the collection, communication, and processing of data, here we introduce a control approach in which the control actions can be computed as a function of the states of the nodes within a limited state information neighborhood. The trade-off between the control performance and the size of this neighborhood is primarily determined by the condition number of the controllability Gramian. Our theoretical results are supported by simulations on regular and random networks and are further illustrated by an application to the control of power-grid synchronization. We demonstrate that for well-conditioned Gramians, there is no significant loss of control performance as the size of the state information neighborhood is reduced, allowing efficient control of large networks using only local information.