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This paper provides observer-based sampled-data and event-triggered boundarycontrol strategies for a class of reaction-diffusion PDEs with collocatedsensing and Robin actuation. Infinite-dimensional backstepping design is usedas the underlying control approach. It is shown that the continuous-time outputfeedback boundary control applied in a sample-and-hold fashion ensures globalclosed-loop exponential stability, provided that the sampling period issufficiently small. Further, robustness to perturbations of the samplingschedule is guaranteed. For the event-triggered implementation of thecontinuous-time controller, a dynamic triggering condition is utilized. Thetriggering condition determines the time instants at which the control inputneeds to be updated. Under the observer-based event-triggered boundary control,it is shown that there is a minimal dwell-time between two triggering instantsindependent of initial conditions. Further, the global exponential convergenceof the closed-loop system to the equilibrium point is established. A simulationexample is provided to validate the theoretical results.

Sampled-Data and Event-triggered Boundary Control of a Class of Reaction-Diffusion PDEs with Collocated Sensing and Actuation