Periodic Event-triggered Boundary Control of a Class of Reaction-Diffusion PDEs

This paper provides a novel periodic event-triggered boundary control (PETBC) strategy for a class of reaction-diffusion PDEs with Robin actuation using infinite-dimensional backstepping boundary control. We propose a method for converting a certain class of continuous-time dynamic event-triggers that require continuous monitoring to periodic event-triggers that require only periodic evaluation. We achieve this by finding an upper bound on the underlying continuous-time event-trigger between two successive periodic evaluations. We provide an explicit criterion for choosing a sampling period for periodically evaluating the event-trigger. The control input is updated only at events indicated by the periodic event-trigger and is applied in a Zero-Order-Hold fashion between two events. We prove that the closed-loop system well-posedness and global L
²
-exponential convergence to zero under continuous-time event-triggered boundary control (CETBC) are preserved under the proposed PETBC. We provide simulation results to validate the theoretical claims.