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The detection and trapping of single fluorescent molecules in solution within a nanochannel is studied using numerical simulations. As optical forces are insufficient for trapping molecules much smaller than the optical wavelength, a means for sensing a molecule's position along the nanochannel and adjusting electrokinetic motion to compensate diffusion is assessed. Fluorescence excitation is provided by two adjacently focused laser beams containing temporally interleaved laser pulses. Photon detection is time-gated, and the displacement of the molecule from the middle of the two foci alters the count rates collected in the two detection channels. An algorithm for feedback control of the electrokinetic motion in response to the timing of photons, to reposition the molecule back toward the middle for trapping and to rapidly reload the trap after a molecule photobleaches or escapes, is evaluated. While accommodating the limited electrokinetic speed and the finite latency of feedback imposed by experimental hardware, the algorithm is shown to be effective for trapping fast-diffusing single-chromophore molecules within a micron-sized confocal region. Studies show that there is an optimum laser power for which loss of molecules from the trap due to either photobleaching or shot-noise fluctuations is minimized.