In nanoscale memristive switching devices, the statistical distribution of resistance values and other relevant parameters for device operation often exhibits a lognormal distribution, causing large fluctuations of memristive analog state variables after each switching event, which may be problematic for digital nonvolatile memory applications. The state variable w in such devices has been proposed to be the length of an undoped semiconductor region along the thickness of the thin film that acts as a tunnel barrier for electronic transport across it. The dynamical behavior of w is governed by the drift diffusion of ionized dopants such as oxygen vacancies. Making an analogy to scanning tunneling microscopes (STM), a closed-loop write scheme using current feedback is proposed to switch the memristive devices in a controlled manner. An integrated closed-loop current driver circuit for switching a bipolar memristive device is designed and simulated. The estimated upper limit of the feedback loop bandwidth is in the order of 100 MHz. We applied a SPICE model built upon the TiO 2 memristive switching dynamics to simulate the single-device write operation and found the closed-loop write scheme caused a narrowing of the statistical distribution of the state variable w.