Stabilization of coupled unstable semilinear reaction-advection-diffusion PDEs with spatially varying coefficients via event-triggered boundary feedback

This paper presents an event-triggered boundary control strategy for a class of unstable $ N $-coupled semilinear reaction-diffusion systems with spatially varying coefficients. The event-triggered control approach consists of a backstepping boundary controller and a triggering condition, which determines the time instants at which the control input needs to be updated. By using event-triggered boundary control, the Zeno behavior is avoided. Further, the well-posedness and the exponential stability of the closed-loop system are established. Finally, some numerical examples are given to verify the effectiveness of the event triggering controller.