Event-triggered Boundary Control of a Class of Reaction-Diffusion PDEs with Time-dependent Reactivity

Abstract: This paper presents an event-triggered boundary control strategy for a class of reaction-diffusion PDEs with time-varying reactivity under Robin actuation. The control approach consists of a backstepping full-state feedback boundary controller and a dynamic event-triggering condition, which determines the time instants when the control input needs to be updated. It is proved that under the proposed event-triggered boundary control approach, there is a uniform minimal dwell-time between two event times. Furthermore, the well-posedness and the global exponential convergence of the closed-loop system to zero in $L^2$-sense are established. A simulation is conducted to validate the theoretical developments.