  This paper provides observer-based sampled-data and event-triggered boundary
control strategies for a class of reaction-diffusion PDEs with collocated
sensing and Robin actuation. Infinite-dimensional backstepping design is used
as the underlying control approach. It is shown that the continuous-time output
feedback boundary control applied in a sample-and-hold fashion ensures global
closed-loop exponential stability, provided that the sampling period is
sufficiently small. Further, robustness to perturbations of the sampling
schedule is guaranteed. For the event-triggered implementation of the
continuous-time controller, a dynamic triggering condition is utilized. The
triggering condition determines the time instants at which the control input
needs to be updated. Under the observer-based event-triggered boundary control,
it is shown that there is a minimal dwell-time between two triggering instants
independent of initial conditions. Further, the global exponential convergence
of the closed-loop system to the equilibrium point is established. A simulation
example is provided to validate the theoretical results.
