High gain limit for boundary controlled convective reaction diffusion equations

Considers a general class of dynamical systems governed by nonlinear partial differential equations of convective reaction diffusion type. Generalizing earlier work for a boundary controlled Burgers' equation, the authors introduce a closed loop boundary control system with dynamics in the state space of square integrable functions on a finite interval. For small square integrable initial data and small time dependent disturbances, the authors show that as the closed loop gains tend to infinity, the trajectories of the closed loop system converge in the mean square sense to the trajectories of the zero dynamics, i.e., the systems obtained by constraining the system output to zero. For slightly stronger assumptions on the external forcing term (disturbance) the authors show that the trajectories converge uniformly.