  We present a detailed theoretical and experimental analysis of Engineered
Swift Equilibration (ESE) protocols applied to two hydrodynamically coupled
colloids in optical traps. The second particle disturbs slightly (10% at most)
the response to an ESE compression applied to a single particle. This effect is
quantitatively explained by a model of hydrodynamic coupling. Then we design a
coupled ESE protocol for the two particles, allowing the perfect control of one
target particle while the second is enslaved to the first. The calibration
errors and the limitations of the model are finally discussed in detail.
