Control of Burgers' Equation With Mixed Boundary Conditions

We consider the problems of simulation and control for Burgers' equation with mixed boundary conditions. We first conduct numerical experiments to test the convergence and stability of two standard finite element schemes for various Robin boundary conditions and a variety of Reynolds numbers. These schemes are used to compute LQR feedback controllers for Burgers' equation with boundary control. Numerical studies of these feedback control laws are used to evaluate the performance and practicality of this approach to boundary control of non-linear systems.