A control problem for Burgers' equation

Abstract

Burgers' equation is a one-dimensional simple model for convection-diffusion phenomena such as shock waves, supersonic flow about airfoils, traffic flows, acoustic transmission, etc. For high Reynolds number, the open-loop system (no control) produces steep gradients due to the nonlinear nature of the convection.

The steep gradients are stabilized by feedback control laws. In this phase, sufficient conditions for the control input functions and the location of sensors are obtained. Also, explicit exponential decay rates for open-loop and closed-loop systems are obtained.

Numerical experiments are given to illustrate some of typical results on convergence and stability.