Finite-dimensional feedback control of a scalar reaction-diffusion equation via inertial manifold theory

Using inertial manifold theory, a finite-dimensional feedback controller is constructed for a nonlinear parabolic partial differential equation so that the dynamics of the closed-loop system is close in a weighted C1-metric for the vector fields to a finite dimensional dynamics prescribed in advance. As a consequence, some structurally stable dynamics, for instance, can be imposed on the controlled system.