Zero dynamics boundary control for regulation of the Kuramoto–Sivashinsky equation

This work is concerned with a problem of tracking regulation for a one-dimensional Kuramoto–Sivashinsky equation. The objective is to design dynamic and static controllers to drive the state of the plant at the ends of the spatial domain to desired reference signals which may be time dependent. The particular case of constant reference signals is referred to as the set point control problem. To solve our tracking problem we employ the zero dynamics inverse design methodology recently developed to solve a variety of tracking and disturbance rejection problems for linear and nonlinear systems. In this paper we describe both dynamic and static control laws and prove that they provide the desired tracking of the reference signals. We also present two numerical examples which illustrate our theoretical results.