Adaptive boundary control of reaction–diffusion PDEs with unknown input delay

Abstract

We design an adaptive full-state feedback controller to stabilize a one-dimensional reaction–diffusion equation with unknown boundary input delay. An infinite-dimensional representation of the actuator delay is utilized to transform the system into a transport PDE cascading with a reaction–diffusion PDE. A suitable parameter update law is designed to establish local boundedness of the system trajectories and asymptotic convergence stability result using the well-known PDE backstepping technique and a Lyapunov argument. Consistent simulation results are provided to support the theoretical results.