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