  To promote the implementation of realistic control over various complex
networks, recent work has been focusing on analyzing energy cost. Indeed, the
energy cost quantifies how much effort is required to drive the system from one
state to another when it is fully controllable. A fully controllable system
means that the system can be driven by external inputs from any initial state
to any final state in finite time. However, it is prohibitively expensive and
unnecessary to confine that the system is fully controllable when we merely
need to accomplish the so-called target control---controlling a subnet of nodes
chosen from the entire network. Yet, when the system is partially controllable,
the associated energy cost remains elusive. Here we present the minimum energy
cost for controlling an arbitrary subset of nodes of a network. Moreover, we
systematically show the scaling behavior of the precise upper and lower bounds
of the minimum energy in term of the time given to accomplish control. For
controlling a given number of target nodes, we further demonstrate that the
associated energy over different configurations can differ by several orders of
magnitude. When the adjacency matrix of the network is nonsingular, we can
simplify the framework by just considering the induced subgraph spanned by
target nodes instead of the entire network. Importantly, we find that, energy
cost could be saved by orders of magnitude as we only need the partial
controllability of the entire network. Our theoretical results are all
corroborated by numerical calculations, and pave the way for estimating the
energy cost to implement realistic target control in various applications.
