Boundary Delayed Observer-Controller Design for Reaction–Diffusion Systems

We consider delayed boundary stabilization of a one-dimensional reaction-diffusion equation under boundary delayed measurements. We design an observer-based control law via the modal decomposition approach. The observer is governed by a partial differential equation, which leads to separation of the observer and the controller design. We suggest a network-based implementation of the controller in the presence of two networks: from sensor to controller, and from the controller to actuator. To reduce the workload of the second network, we suggest a novel switching-based dynamic event-triggering mechanism. We extend the results to the vector case and illustrate their efficiency by a numerical example.