Reduced Order Controller Design for Robust Output Regulation of Parabolic Systems

We study robust output regulation for linear parabolic control systems. As our main results we show that robust output tracking and disturbance rejection for this class of PDE models can be achieved using a finite-dimensional controller and present algorithms for construction of two different internal model based robust controllers. The controller parameters are chosen based on Galerkin approximations of the original PDE system and employ balanced truncation to reduce the orders of the controllers. In the second part of the paper we design controllers for robust output tracking and disturbance rejection for a 1D reaction-diffusion equation with boundary disturbances, a 2D diffusion-convection equation, and a damped 1D beam equation.