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<p>This paper addresses boundary control to input-to-state stabilization for fractional convection-diffusion-reaction (FCDR) systems governed by coupled time fractional partial differential equations (TFPDEs) under matched and unmatched disturbances over actuator/sensor networks using output feedback, fractional sliding mode (FSM) algorithm and sampled-in-space sensing. Here it is assumed that sensors provide discrete in space measurements, i.e., spatially averaged measurements (SAMs), and a limited number of sensors are allocated in a spatial domain. A sampled-data observation problem is first in investigation, which contains to design an FSM observer against boundary disturbances and to prove input-to-state stability (ISS) of the proposed observer. Using this observer and backstepping approach, the authors develop an output feedback FSM controller and establish the reaching condition to FSM surface. Using the fractional Lyapunov method, ISS of the closed-loop dynamics is achieved. Theoretical results are verified by numerical simulations.</p>

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Input-to-State Stabilization of Coupled Time Fractional PDEs Using Observer-Based Fractional Sliding Mode Control and Sampled Measurements

  • 期刊论文

  • 发表日期：

    2025年12月13日

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  • Juan Chen,
  • Yuwei Xue,
  • Hua-Cheng Zhou,
  • Bo Zhuang

摘要

This paper addresses boundary control to input-to-state stabilization for fractional convection-diffusion-reaction (FCDR) systems governed by coupled time fractional partial differential equations (TFPDEs) under matched and unmatched disturbances over actuator/sensor networks using output feedback, fractional sliding mode (FSM) algorithm and sampled-in-space sensing. Here it is assumed that sensors provide discrete in space measurements, i.e., spatially averaged measurements (SAMs), and a limited number of sensors are allocated in a spatial domain. A sampled-data observation problem is first in investigation, which contains to design an FSM observer against boundary disturbances and to prove input-to-state stability (ISS) of the proposed observer. Using this observer and backstepping approach, the authors develop an output feedback FSM controller and establish the reaching condition to FSM surface. Using the fractional Lyapunov method, ISS of the closed-loop dynamics is achieved. Theoretical results are verified by numerical simulations.