Control of dissipative partial differential equation systems using APOD based dynamic observer designs

This article focuses on output feedback control of distributed parameter systems with limited number of sensors employing adaptive proper orthogonal decomposition (APOD) methodology. The controller design issue is addressed by combining a robust state controller with a dynamic observer of the system states to reduce sensor requirements. The use of APOD methodology allows the development of locally accurate low-dimensional reduced order dynamic models (ROMs) for controller synthesis thus resulting in a computationally-efficient alternative to using large-dimensional models with global validity. The derived ROMs are subsequently employed for the design of dynamic observers and controllers. The proposed methods are successfully used to achieve the desired control objective of stabilizing the Kuramoto-Sivashinksy equation (KSE) at a desired state spatial profile.