Flow maldistribution, resulting from bubbles or other particulate matter, can lead to drastic performance degradation in devices that employ parallel microchannels for heat transfer. In this work, direct numerical simulations of fluid flow through a prescribed parallel microchannel geometry are performed and coupled with active control of actuated microvalves to effectively identify and reduce flow maldistribution. Accurate simulation of fluid flow through a set of three parallel microchannels is achieved utilizing a fictitious-domain representation of immersed objects such as microvalves and artificially introduced bubbles. Flow simulations are validated against experimental results obtained for flow through a single high-aspect ratio microchannel, flow around an oscillating cylinder, and flow with a bubble rising in an inclined channel. Results of these simulations compare very well to those obtained experimentally, and validate the use of the solver for the parallel microchannel configuration of this study. System identification techniques are employed on numerical simulations of fluid flow through the geometry to produce a lower dimensional model that captures the essential dynamics of the full nonlinear flow, in terms of a relationship between valve angles and the exit flow rate for each channel. A model-predictive controller is developed, which employs this reduced order model to identify flow maldistribution from exit flow velocities and to prescribe actuation of channel valves to effectively redistribute the flow. Flow simulations with active control are subsequently conducted with artificially introduced bubbles. The model-predictive control methodology is shown to adequately reduce flow maldistribution by quickly varying channel valves to remove bubbles and to equalize flow rates in each channel.