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Sliding mode control for the stabilization of fractional heat equations subject to boundary uncertainty

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  • Cai, Rui-Yang
  • Cheng, Lan
  • Zhou, Hua-Cheng

Abstract

By adopting the sliding mode control (SMC) and the generalized Lyapunov method, the boundary feedback stabilization issue is studied for the fractional diffusion system subject to boundary control matched disturbance. The classical sliding surface and the fractional integral sliding function are constructed and sliding mode controllers are designed respectively to realize the Mittag-Leffler (M-L) stabilization of the considered system. The controller based on the newly-introduced fractional integral sliding function not only helps to relax the constraints on the disturbance but also realizes the same stabilization effect as that of the classical one. The well-posedness result of the solution is also obtained for discontinuous fractional heat equations. Besides, a numerical experiment validates the theoretical outcomes.

Suggested Citation

  • Cai, Rui-Yang & Cheng, Lan & Zhou, Hua-Cheng, 2024. "Sliding mode control for the stabilization of fractional heat equations subject to boundary uncertainty," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924002704
    DOI: 10.1016/j.chaos.2024.114718
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    References listed on IDEAS

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    1. Jiang, Jingfei & Guirao, Juan Luis García & Chen, Huatao & Cao, Dengqing, 2019. "The boundary control strategy for a fractional wave equation with external disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 92-97.
    2. Meerschaert, Mark M. & Mortensen, Jeff & Wheatcraft, Stephen W., 2006. "Fractional vector calculus for fractional advection–dispersion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 181-190.
    3. Cai, Rui-Yang & Zhou, Hua-Cheng & Kou, Chun-Hai, 2021. "Boundary control strategy for three kinds of fractional heat equations with control-matched disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
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