  We analyze the control of the motion of a charged particle by means of an
external electric field. The system is constrained to move along a given
direction. The goal of the control is to change the speed of the particle in a
fixed time with zero initial and final accelerations, while minimizing a cost
functional in order to achieve a smooth transport of the system. We solve this
linear control problem by using shortcut to adiabaticity methods and optimal
control techniques. STA protocols are built upon local constraints. By
extending the number of space variables, we explain how optimal control
protocols can accommodate for such constraints and provide robust solutions
against slight initial and final time uncertainties. Conversely, optimal
control can guide the choice of the class of functions involved in STA
processes. Such mutual benefices of the two approaches remain valid beyond the
specific example studied here.
