  We consider the control of discrete-time linear dynamical systems using
sparse inputs where we limit the number of active actuators at every time step.
We develop an algorithm for determining a sparse actuator schedule that ensures
the existence of a sparse control input sequence, following the schedule, that
takes the system from any given initial state to any desired final state. Since
such an actuator schedule is not unique, we look for a schedule that minimizes
the energy of sparse inputs. For this, we optimize the trace of the inverse of
the resulting controllability Gramian, which is an approximate measure of the
average energy of the inputs. We present a greedy algorithm along with its
theoretical guarantees. Finally, we empirically show that our greedy algorithm
ensures the controllability of the linear system with a small number of active
actuators per time step without a significant average energy expenditure
compared to the fully actuated system.
