Feedback Control of Instabilities in Hydrodynamic Systems

Abstract

<p>This dissertation is concerned with the development of a linear control strategy for stabilization of unstable solutions of the lD Kuramoto-Sivashinsky equation in a periodic domain. This equation serves as a simple model for hydrodynamic system. The KuramotoSivashinsky equation is solved using a spectral method in both steady and unsteady regime, which is described. Computational results show the existence of several families on steady solutions, some of which are unstable. The unstable solutions are stabilized using the Linear-Quadratic-Gaussian algorithm. The feedback operators are determined by solving the matrix Riccati equation. In the thesis we also analyze computationally the effectiveness of the feedback stabilization algorithm depending on various parameters.</p>