A presently realizable picosecond half-cycle electromagnetic pulse (HCP) consists of a short (<1 ps) unipolar part followed by a long ( ∼  100 ps), much weaker unipolar part of opposite polarity. In this work we investigate the quantum dynamics and emission properties of an electron driven by a train of HCP's in an Al_xGa_1−xAs based symmetric double quantum well. Our full numerical results, analyzed with the aid of a simple analytical model, show that an appropriately designed train of HCP's allows the coherent control of the electron motion on a subpicosecond scale, i.e., the electron can be driven to achieve and maintain a predefined final state for hundreds of picoseconds. We further show that it is possible to engineer the emission spectrum by an appropriate choice of HCP's parameters. Consequences of the absence of the generalized parity of the Floquet modes on the dynamics of the system are discussed. Phenomena such as coherent suppression of tunneling in the absence of accidental degeneration of quasienergies, low-frequency generation, and half-harmonic generation are observed. An estimate of the pulse parameters that allows the efficient control of the electron motion and its emission spectrum are derived from a simplified analytical model.