  Controlling many-body quantum systems is a highly challenging task required
to advance quantum technologies. Here, we report progress in controlling
gapless many-body quantum systems described by the Tomonaga-Luttinger liquid
(TLL). To do so, we investigate the exact dynamics of the TLL induced by an
interaction quench, making use of the $SU(1,1)$ dynamical symmetry group and
the Schr\"odinger picture. First, we demonstrate that this approach is useful
to perform a shortcut to adiabaticity, that cancels the final non-adiabatic
residual energy of the driven TLL and is experimentally implementable in the
semiclassical limit of the sine-Gordon model. Second, we apply this framework
to analyze various driving schemes in finite time, including linear ramps and
smooth protocols.
