Robust control of parabolic PDE systems with time-dependent spatial domains

Robust nonlinear static output feedback controllers were synthesized for systems of quasi-linear parabolic partial differential equations with time-dependent spatial domains and uncertain variables. The developed controllers guarantee boundedness of the state and output tracking with arbitrary degree of asymptotic attenuation of the effect of the uncertain parameters on the controlled output of the closed loop system, provided that the separation between the slow and fast dynamical phenomena is sufficiently large. The controllers were successfully applied to a typical diffusion-reaction process with moving boundary and time-varying uncertainty and were shown to outperform controllers that do not account for the presence of the uncertainty.