Boundary layer control for the viscous Burgers' equation

In this paper we consider the problem of Dirchlet boundary control for the viscous Burgers' equation. The focus here is on reducing the energy in the flow near the boundary. This problem is similar to the problem of controlling the boundary layer in fluid flows. The near wall flow is controlled by applying an optimal feedback law derived from distributed parameter theory. It is shown that this optimal feedback controller is local in space and the form of the control law is then exploited to design a practical controller. In particular, the controller is constructed by approximating the functional gains that define the feedback law. Numerical examples are presented to illustrate the effectiveness of the method.