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

• Published in: Applied mathematics and computation Vol. 478; p. 128830
• Main Authors: Ge, Fudong, Chen, YangQuan
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.10.2024
• Subjects: Boundary control; Event-triggered control; Fractional-order partial differential equations; Spatially-varying coefficients; Time-fractional diffusion systems; Boundary control; Event-triggered control; Fractional-order partial differential equations; Time-fractional diffusion systems; Spatially-varying coefficients
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2024.128830

In this paper, an event-triggered control scheme is proposed for boundary controlled time-fractional 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 well-posedness 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. •Different from existing works, this paper aims to address event-triggered boundary control of time fractional diffusion systems.•The sufficient conditions for Mittag-Leffler stability of corresponding closed-loop systems are carefully derived.•The non-occurrence of so-called Zeno behavior for our proposed event-triggered boundary controller is seriously proven.