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

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  • Ge, Fudong
  • Chen, YangQuan

Abstract

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.

Suggested Citation

  • Ge, Fudong & Chen, YangQuan, 2024. "Event-triggered control for boundary controlled time-fractional diffusion systems with spatially-varying coefficients," Applied Mathematics and Computation, Elsevier, vol. 478(C).
    • Handle: RePEc:eee:apmaco:v:478:y:2024:i:c:s0096300324002911
    DOI: 10.1016/j.amc.2024.128830
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    References listed on IDEAS

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    1. Yao, Xiuming & Lian, Yue & Park, Ju H., 2019. "Disturbance-observer-based event-triggered control for semi-Markovian jump nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    2. Li, Xin & Mu, Xiaowu, 2024. "Dynamic event-triggered fuzzy control for nonlinear singular semi-Markovian jump systems via state decomposition approach," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    3. Mathiyalagan, K. & Nidhi, A. Shree & Su, H. & Renugadevi, T., 2022. "Observer and boundary output feedback control for coupled ODE-transport PDE," Applied Mathematics and Computation, Elsevier, vol. 426(C).
    4. Fu, Yingying & Li, Jing & Li, Xiaobo & Wu, Shuiyan, 2023. "Dynamic event-triggered adaptive control for uncertain stochastic nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 444(C).
    5. Li, Mingyue & Wang, Mingzhu & Liu, Wenlu & Wu, Shuchen & Li, Xiaodi, 2023. "Exponential stability of nonlinear systems via event-triggered impulsive control based on partial states," Applied Mathematics and Computation, Elsevier, vol. 459(C).
    6. Song, Xiaona & Zhang, Renzhi & Song, Shuai & Zhang, Yijun, 2022. "Fuzzy adaptive-event-triggered control for semi-linear parabolic PDE systems with stochastic actuator failures," Applied Mathematics and Computation, Elsevier, vol. 426(C).
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