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

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 con...

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Vydáno v:Chaos, solitons and fractals Ročník 181; s. 114718
Hlavní autoři: Cai, Rui-Yang, Cheng, Lan, Zhou, Hua-Cheng
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.04.2024
Témata:
Disturbance rejection
Mittag-Leffler stabilization
Sliding mode control
Well-posedness of discontinuous systems
Disturbance rejection
37L15
35B35
93D15
Well-posedness of discontinuous systems
Mittag-Leffler stabilization
93B52
Sliding mode control
93B51
ISSN:0960-0779, 1873-2887
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Popis
Shrnutí: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. •The well-posedness of fractional PDEs with discontinuous boundary is proved.•The constraint on the coefficient is relaxed.•The classical sliding surface and a fractional integral sliding function are given.•The range for the external disturbance is broadened.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2024.114718