Reduced-order-based feedback control of the Kuramoto-Sivashinsky equation

Authors:
C. H. Lee;H. T. Tran
Affiliations:
Department of Mathematics, California State University, Fullerton, CA;Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

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Abstract

In this paper, we consider the Kuramoto-Sivashinsky equation (KSE), which describes the long-wave motions of a thin film over a vertical plane. Solution procedures for the KSE often yield a large or infinite-dimensional nonlinear system. We first discuss two reduced-order methods, the approximate inertial manifold and the proper orthogonal decomposition, and show that these methods can be used to obtain a reduced-order system that can accurately describe the dynamics of the KSE. Moreover, from this resulting reduced-order system, the feedback controller can readily be designed and synthesized. For our control techniques, we use the linear and nonlinear quadratic regulator methods, which are the first- and second-order approximated solutions of the Hamilton-Jacobi-Bellman equation, respectively. Numerical simulations comparing the performance of the reduced-order-based linear and nonlinear controllers are presented.