In recent years the interest in control of distributed parameter systems (DPSs) has significantly increased in the chemical and advanced material process industries. This is due to the need to synthesize control structures for complex transport-reaction processes which are characterized by the coupling of chemical reactions with significant convection, diffusion, and dispersion phenomena. Such processes as exemplified by packed and fluidized bed reactors in chemical plants, reactive distillation in petrochemical industries processes, most lithographic and deposition processes in microelectronics and advanced materials manufacturing, and finally crystal and glass production, exhibit spatial variations that need to be explicitly accounted for by the controller.An important observation is that the long term behavior of the above chemical processes can be captured by a finite number of degrees of freedom; thus the partial differential equation (PDE) descriptions can be effectively approximated by reduced order models (ROMs) in the form of finite dimensional ordinary differential equations (ODEs). For processes with nonlinear spatial operators and/or complex process domains, the ODEs can only be obtained via data-driven order reduction methods. Their major shortcoming is that they require a representative ensemble of solutions pre-exists for the process to be properly described, while there isn't a systematic method to ensure this important prerequisite. Currently, there is a lack of systematic and computationally-efficient data-driven methodologies for optimization and control of nonlinear PDE systems with complex spatial domains.The proposed research will extend the applicability of control-oriented data-driven nonlinear order reduction methods for dissipative nonlinear PDE systems. The intellectual objective is to relax the requirement of a representative ensemble of solutions and develop a systematic data-driven order reduction methodology specifically tailored for control of PDE systems. It will thus resolve a fundamental limitation of data-driven techniques for control synthesis of spatially distributed processes. The main contributions of the proposed research can be classified as (a) deriving a computationally efficient adaptive model order reduction framework to circumvent the limitations of the current model order reduction techniques for control of nonlinear DPSs, and (b) synthesizing advanced output feedback control structures that can guarantee closed-loop stability and performance while (c) identifying criteria to minimize the required information for the controller structure revisions.