Input-to-state stabilization of coupled time fractional PDEs using observer-based fractional sliding mode control and sampled measurements

CHEN Juan, XUE Yuwei, ZHOU Hua-Cheng, ZHUANG Bo

Journal of Systems Science & Complexity ›› 2025

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PDF(1317 KB)
Journal of Systems Science & Complexity ›› 2025

Input-to-state stabilization of coupled time fractional PDEs using observer-based fractional sliding mode control and sampled measurements

  • CHEN Juan1, XUE Yuwei1, ZHOU Hua-Cheng2, ZHUANG Bo3
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Abstract

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 a FSM observer against boundary disturbances and to prove input-to-state stability (ISS) of the proposed observer. Using this observer and backstepping approach, we 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.

Key words

Input-to-state stability / fractional PDEs / fractional sliding mode control / output feedback / sampled measurements

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CHEN Juan , XUE Yuwei , ZHOU Hua-Cheng , ZHUANG Bo. Input-to-state stabilization of coupled time fractional PDEs using observer-based fractional sliding mode control and sampled measurements. Journal of Systems Science & Complexity, 2025

Funding

This research was supported by National Natural Science Foundation of China (62203070, 12161141013, 62173348), Jiangsu Government Scholarship for Studying Abroad (SCZ2307400004), Jiangsu Innovation Program for Graduates (KYCX23 3068) and the science and technology project of Changzhou University (KYP2202225C).
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