Control of 2-D reaction-advection-diffusion PDE with input delay

This paper designs a boundary controller for a reaction-advection-diffusion equation on the cylindrical surface with input delay. We introduce a transport partial differential equation (PDE) to remove the input delay by transforming the time delay into a spatial travelling. Then the system with time delay turns to a cascade system composed of two PDEs without delay. For the cascade system, we design boundary control by applying the PDE backstepping method and find the feedback gain function. The Lyapunov function is defined and used to prove the exponential stability of the controlled system in H
²
norm. The numerical simulations show that the closed-loop system converges to zero, which illustrates the effectiveness of the proposed method.