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

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. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

An adaptive full-state feedback controller was designed to stabilize a one-dimensional reaction-diffusion equation with unknown boundary input delay. The system was transformed into a transport PDE cascading with a reaction-diffusion PDE using an infinite-dimensional representation of the actuator delay, and a suitable parameter update law was designed to establish local boundedness and asymptotic convergence stability. Consistent simulation results were provided to support the theoretical findings.