  Recently it has been shown that the control energy required to control a
dynamical complex network is prohibitively large when there are only a few
control inputs. Most methods to reduce the control energy have focused on
where, in the network, to place additional control inputs. Here, in contrast,
we show that by controlling the states of a subset of the nodes of a network,
rather than the state of every node, while holding the number of control
signals constant, the required energy to control a portion of the network can
be reduced substantially. The energy requirements exponentially decay with the
number of target nodes, suggesting that large networks can be controlled by a
relatively small number of inputs as long as the target set is appropriately
sized. We validate our conclusions in model and real networks to arrive at an
energy scaling law to better design control objectives regardless of system
size, energy restrictions, state restrictions, input node choices and target
node choices.

Systems and Control;Physics and Society