Abstract.
We consider the problem of defining an optimal strategy to control a dynamical complex network, optimal in terms of a general cost function. Here we show that by controlling a network's output rather than the state of every node, the required energy to control the network can be reduced substantially. In particular, by only targeting a subset of the nodes of the network, the energy requirements exponentially decay. We also show that the minimum energy well-approximates the energy required for a large family of cost objectives so that the benefits of target control extend beyond the minimum energy control scheme considered in the literature. 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, driver node choices and target node choices.
Though this formulation is very general and could be applied in principle to a great variety of social, technological, and biological networks, here we focus on cell signaling networks, where control inputs are supplied drugs and target and driver nodes are appropriately chosen molecules. As an example of an application, we study control of the mechanism responsible for the orderly degradation and recycling of cellular components, known as autophagy (literally, the cell eats itself ). For this case, we show how the required control energy can vary, based on the choice of driver and target nodes.