We address the problem of control of spatially distributed processes in the presence of measurement constraints. Specifically, we assume the availability of sensors that measure part of the state spatial profile. The measurements are utilized for the derivation and on-demand update of reduced order models (ROM) based on an extension of the adaptive proper orthogonal decomposition (APOD) method using a snapshot reconstruction technique. The proposed Gappy-APOD methodology constructs locally accurate low-dimensional ROM thus resulting in a computationally efficient alternative to using a large-dimensional ROM with global validity. Based on the low-dimensional ROM and continuous measurements available from point sensors a Lyapunov-based static output feedback controller is subsequently designed. The proposed controller design method is illustrated on an unstable process modeled by the Kuramoto-Sivashinsky equation, when the designed controller successfully stabilizes the process even in the presence of model uncertainty. (C) 2012 American Institute of Chemical Engineers AIChE J, 59: 747-760, 2013