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This work employs adaptive reduced order models (ROMs) in the design of model predictive controllers for stabilization of processes that are mathematically expressed as parabolic partial differential equation (PDE) systems. Initially, we construct a locally valid ROM of the PDE system employing the basis functions computed by applying an adaptive model reduction methodology called APOD on a small data ensemble. This ROM is then utilized in the design of model predictive controllers (MPC) under constraints on the control action. As periodic closed-loop process data becomes available (during closed-loop operation under the constructed MPC), we recursively update the ROM by employing our computationally efficient adaptive model reduction methodology thus extending the validity of ROM over the current operating region. The effects of employing the adaptive methodology on performance of MPC is studied. The design of such MPC controllers is illustrated by employing the methodology on numerical simulations.