A framework is introduced for the identification of controls for single-class time-varying queueing networks that are asymptotically optimal in the so-called uniform acceleration regime. A related, but simpler, first-order (or fluid) control problem is first formulated. For a class of performance measures that satisfy a certain continuity property, it is then shown that any sequence of policies whose performances approach the infimum in the fluid control problem is asymptotically optimal for the original network problem. Examples of performance measures with this property are described, and simulations implementing asymptotically optimal policies are presented. The use of directional derivatives of the reflection map for solving fluid control problems is also illustrated. This work serves to complement a large body of literature on asymptotically optimal controls for time-homogeneous networks.