Event-Triggered Output-Feedback Control of the 1-D Parabolic PDE Systems with Spatially-Varying Coefficient

This paper investigates the event-triggered control problem for scalar parabolic PDE systems with spatially-varying coefficient and Dirichlet boundary actuation. The proposed control strategy only relies on boundary measurements. A nominal output-feedback backstepping controller is designed based on a state observer. Then, the dynamic event-triggered conditions are developed to determine the control update instants. It is further shown that the proposed event-triggered mechanism can guarantee a minimum dwell time. Stability of the closed-loop system is analyzed, and the pointwise convergence of the state is established. Finally, numerical simulations are given to demonstrate the effectiveness of this approach.