Jet flow control is important for mixing enhancement and noise mitigation. In previous efforts, we have used validated simulations to examine the effect of localized arc filament plasma actuators (LAFPA) on perfectly expanded Mach 1.3 jets. Here, we extend the analysis to an underexpanded jet at the same Mach number to examine the effect of shocks and expansions on control authority. After validation of the baseline flow, it is shown that the downstream evolution is relatively independent of Reynolds number. Simulations performed at different values of upstream pressure indicate that the higher stagnation pressure yields shock cells that are quantitatively stronger but qualitatively similar to those observed for the lower upstream stagnation pressure condition. For control simulations, axisymmetric mode pulsing is considered at two different Strouhal numbers of St = 0.3 and St = 0.9. These simulations show that the response of the jet to flow control is a strong function of the actuation frequency. Relative to the no-control case, actuating at the column-mode instability frequency (St = 0.3) results in an increase in the rate of spreading of the shear layer. Phase-averaged results indicate the formation of large toroidal vortices formed as a result of amplification of the column-mode instabilities that are excited at this frequency. On the other hand, the higher frequency actuation affects the initial shear-layer instability and interferes with the formation of the large-scale structures. Detailed integral azimuthal length scale analyses reveal that despite the absence of the axisymmetric toroids, the St = 0.9 case shows the dominance of the axisymmetric mode even at large distances from the nozzle exit. This indicates that flow control methods need not always have a visual signature of their influence on the system.