On global stabilization of Burgers' equation by boundary control

Burgers' equation is a natural first step towards developing methods for control of flows. We derive nonlinear boundary control laws that achieve global asymptotic stability (in a very strong sense). We consider both the viscous and the nonviscous Burgers' equation, using both Neumann and Dirichlet boundary control. We also study the case where the viscosity parameter is uncertain, as well as the case of stochastic Burgers' equation. For some of the control laws that would require the measurement in the interior of the domain, we develop the observer-based versions.