Bounded output feedback control of the Kuramoto-Sivashinsky equation with input constraints

This work focuses on the stabilization of the Kuramoto-Sivashinsky equation (KSE) with periodic boundary conditions at the zero solution in the presence of input constraints. Bounded nonlinear stabilizing controllers are synthesized on the basis of finite-dimensional Galerkin approximations of the KSE which capture the dominant dynamics of the equation for a given value of the instability parameter. The controller design accounts explicitly for the presence of input constraints and an explicit characterization of the limitations imposed by the input constraints on the allowable control actuator locations is provided. The theoretical results are successfully illustrated through computer simulations of the closed-loop system using a high-order discretization of the KSE.