Boundary delayed observer-controller design for reaction-diffusion systems

We consider delayed boundary stabilization of a 1D 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 PDE 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.