By exploiting Landau-Zener-Stückelberg (LZS) interference in double quantum dots, we have demonstrated a complete control of the quantum dot charge qubit on the time scales of picoseconds, orders of magnitude faster than those previously measured in the electrically-controlled charge or spin based qubits.We observe tunable qubit dynamics in a charge stability diagram, in a time domain, and in a pulse amplitude space of the driven pulse.These results establish the feasibility of a full set of ali-electrical single qubit operations.Although our experiment is carried out in a solid-state architecture, the technique is independent of the particular physical encoding of quantum information, and has the potential for wider applications.