Reduced Order Controller Design for Robust Output Regulation

We study robust output regulation for parabolic partial differential equations (PDEs) and other infinite-dimensional linear systems with analytic semigroups. As our main results, we show that robust output tracking and disturbance rejection for our class of systems 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 a Galerkin approximation 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 one-dimensional (1D) reaction-diffusion equation with boundary disturbances, a 2D diffusion-convection equation, and a 1D beam equation with Kelvin-Voigt damping.