Event-triggered control for boundary controlled time-fractional diffusion systems with spatially-varying coefficients

In this paper, an event -triggered control scheme is proposed for boundary controlled timefractional diffusion systems with a semilinear function and the spatially -varying coefficients. Toward this aim, backstepping method is utilized. The use of backstepping allows us to explicitly express our proposed event -triggered boundary controllers. Specifically, we first discuss wellposedness of the solution to the problem under consideration. An event -triggered boundary controller is then designed using backstepping to Mittag-Leffler stabilize the system under consideration. After these, we show that our event -triggered controller can efficiently prevent the existence of so-called Zeno phenomenon. Finally, we give a numerical example to illustrate the effectiveness of designed event -triggered boundary control scheme.