We consider the output tracking problem of spatially distributed processes described by nonlinear dissipative partial differential equations (DPDEs). The infinite dimensional representation of such systems can be decomposed to finite dimensional slow and infinite dimensional fast and stable subsystems. To circumvent the important issues of controller and observer synthesis for large dimensional models of DPDEs, the controller and observer design is addressed using adaptive proper orthogonal decomposition (APOD) to recursively construct locally accurate low dimensional reduced order models. The effectiveness of the proposed control structure is successfully illustrated on an output tracking problem of thermal dynamics in a catalytic reactor to reduce hot spot temperature and manage the thermal energy distribution across reactor length using limited number of actuators and sensors.