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Disturbance observer and Mittag-Leffler stabilization design for multi-dimensional fractional distributed parameter systems

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  • Zhou, Hua-Cheng
  • Qian, Jun-Yan
  • Cai, Rui-Yang

Abstract

We consider the boundary output feedback Mittag-Leffler (M-L) stabilization of a spatial multi-dimensional time fractional distributed parameter systems (DPSs), where the control input is actuated by Neumann boundary control input with the external disturbance. By employing the active disturbance rejection control (ADRC) approach, we design a disturbance observer consisting of two subsystems in light of the boundary output signal. The first one is utilized to channel the unknown disturbance to a stable system so that the second can observe the unknown disturbance. By employing the fractional Lyapunov method, the bounded disturbance observer can well estimate the external disturbance which means the observation error decays to zero in H1/2(Γ1). Then a disturbance-observer-based stabilizing controller is proposed to ensure the M-L stability of the original system part in the closed-loop system. Finally, some simulations are included to demonstrate the theoretical results.

Suggested Citation

  • Zhou, Hua-Cheng & Qian, Jun-Yan & Cai, Rui-Yang, 2024. "Disturbance observer and Mittag-Leffler stabilization design for multi-dimensional fractional distributed parameter systems," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    • Handle: RePEc:eee:apmaco:v:470:y:2024:i:c:s009630032400033x
    DOI: 10.1016/j.amc.2024.128561
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    1. Sun, Li & Shen, Jiong & Hua, Qingsong & Lee, Kwang Y., 2018. "Data-driven oxygen excess ratio control for proton exchange membrane fuel cell," Applied Energy, Elsevier, vol. 231(C), pages 866-875.
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