The output feedback control of distributed parameter systems based on adaptive model reduction is explored in this paper. A significant computational hurdle when using model reduction for control (MRC) is the numerical computation of integrals that appear in the reduced order model limiting MRC's applicability when dealing with nonlinearities. The objective of this paper is to further reduce the computational cost in adaptive proper orthogonal decomposition (APOD). It is addressed by using discrete empirical interpolation method (DEIM) in the observer and controller to reduce the computational cost associated with the nonlinear functions. The proposed method is successfully illustrated on a diffusion reaction process and a fluid flow system described by the Kuramoto-Sivashinsky equation.