Structured spatial control of the reaction-diffusion equation with parametric uncertainties

Feedback control problems for distributed parameter systems arise in a variety of physical, chemical, biological, and mechanical systems. This paper exploits the algebraic structure of the system of ordinary differential equations that arise from spatial discretization of the partial differential equation (PDE) to analyze and design feedback controllers that are robust to bounded perturbations in the parameters of the original PDE. As a prototypical problem, this paper investigates the spatial field control of a reaction-diffusion system whose spatial discretization has a state matrix that is circulant symmetric. Structured robust controllers are designed based on internal model control and mixed sensitivity optimization. The controllers are shown to be robust to inaccuracies in the spatial manipulation, even for arbitrarily fine spatial discretizations.