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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| Published in | Chaos, solitons and fractals Vol. 181; p. 114718 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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01.04.2024
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| 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.
•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. |
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| AbstractList | 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. |
| ArticleNumber | 114718 |
| Author | Cheng, Lan Cai, Rui-Yang Zhou, Hua-Cheng |
| Author_xml | – sequence: 1 givenname: Rui-Yang orcidid: 0000-0001-8385-2329 surname: Cai fullname: Cai, Rui-Yang organization: College of Science, University of Shanghai for Science and Technology, Shanghai 200093, PR China – sequence: 2 givenname: Lan surname: Cheng fullname: Cheng, Lan organization: School of Mathematics and Statistics, Central South University, Changsha, 410075, PR China – sequence: 3 givenname: Hua-Cheng orcidid: 0000-0001-6856-2358 surname: Zhou fullname: Zhou, Hua-Cheng email: hczhou@amss.ac.cn organization: School of Mathematics and Statistics, Central South University, Changsha, 410075, PR China |
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| Keywords | Disturbance rejection 37L15 35B35 93D15 Well-posedness of discontinuous systems Mittag-Leffler stabilization 93B52 Sliding mode control 93B51 |
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| Snippet | By adopting the sliding mode control (SMC) and the generalized Lyapunov method, the boundary feedback stabilization issue is studied for the fractional... |
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| SubjectTerms | Disturbance rejection Mittag-Leffler stabilization Sliding mode control Well-posedness of discontinuous systems |
| Title | Sliding mode control for the stabilization of fractional heat equations subject to boundary uncertainty |
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