Control Theory seminar | Rasha Jamal, A Single Bounded Input Control to the Kuramoto-Sivashinsky EquationExport this event to calendar

Thursday, April 11, 2013 — 1:30 PM EDT

MC 5158

Speaker

Rasha Jamal, Applied Mathematics, University of Waterloo

Title

A Single Bounded Input Control to the Kuramoto-Sivashinsky Equation

Abstract

The Kuramoto-Sivashinsky (KS) equation is a nonlinear partial differential equation that is first-order in time and fourth-order in space. It models reaction-diffusion systems and is related to various pattern formation phenomena where turbulence or chaos appear. For instance, it models long wave motions of the liquid film over a vertical plane. For certain parameter values of interest, this equation is unstable. This is shown by analyzing the stability of the linearized system and showing that the nonlinear C0-semigroup corresponding to the nonlinear system is Frechet differentiable. There are a number of papers establishing the stabilization of this equation via boundary control. In this talk, we consider distributed control with a single control variable for the KS equation with periodic boundary conditions. First, we show that stabilizing the linearized KS equation implies local exponential stability of the KS equation. This is done by establishing Frechet differentiability of the associated semigroup and showing that it is equal to the semigroup generated by the linearization of the equation. Next, we construct a single input-feedback control that locally exponentially stabilizes the KS equation. Finally, we control the KS equation from one equilibrium solution to another.

Location 
University of Waterloo
MC 5158

,
Canada

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