We consider a typical semiconductor resonant tunnelling GaAs/AlGaAs/GaAs nanostructure which forms a double-barrier potential with quasienergy levels corresponding to transition frequencies in the infrared and microwave regions. Two types of dynamical perturbation of the heterostructure in the form and are considered. We analyse numerically a reconstruction of the electron transmission through the heterostructure and the current - voltage characteristics (IVC) under the influence of these dynamical perturbations. Both weak and strong perturbations are considered. We investigate the dependences of the transmission on the electron energy and the frequency of the external field with the main accent on the case where a frequency of the perturbation is tuned to a transition between quasienergies of the double-barrier structure. It is found that these resonant phenomena give rise to new peaks and dips in the IVC. In particular, it is shown that the dipole type of perturbation gives rise to a Rabi splitting of the transmission peaks and under certain conditions to a Rabi splitting of the IVC peaks and dips. We demonstrate that dynamical perturbation may induce a direct current opposite to the direction of the applied voltage, and that this phenomenon takes the form of a sharp dip which has a resonant origin. It is observed that the dipole type of perturbation of laser radiation is more effective for tuning the IVC than the first perturbation . Also absorption and emission of energy by an electron transmitted through the DBRTS are considered.