Adaptive Control of Reaction-Advection-Diffusion PDEs with Distributed Actuation and Unknown Input Delay*

We consider a system of a reaction-advection-diffusion partial differential equation (PDE) with a distributed input subject to an arbitrarily large and unknown time-delay. Using Lyapunov technique, we derive an adaptive controller and design a suitable update law to ensure the global stability of the closed-loop system in the L2 sense.