Wave suppression by nonlinear finite-dimensional control

Korteweg-de Vries-Burgers (KdVB) and Kuramoto-Sivashinsky (KS) equations are two nonlinear partial differential equations (PDEs) which can adequately describe motion of waves in a variety of fluid flow processes. We synthesize nonlinear finite-dimensional output feedback controllers for the KdVB and KS equations that enhance convergence rate and achieve stabilization to spatially uniform steady-states, respectively. The controllers use measurements obtained by point sensors and are implemented through point control actuators. The performance of the proposed controllers is successfully tested through simulations.