Boundary disturbance rejection for fractional distributed parameter systems via the sliding mode and Riesz basis approach

We study the sliding mode control (SMC) design for unstable fractional heat and wave equations involving unknown external disturbances, respectively. In the case that the disturbance vanishes, a backstepping transform is constructed at first to stabilize the considered system in Mittag-Leffler (M-L)...

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Bibliographic Details
Published in:Nonlinear dynamics 2023, Vol.111 (2), p.1355-1367
Main Authors: Cai, Rui-Yang, Zhou, Hua-Cheng, Kou, Chun-Hai
Format: Article
Language:English
Subjects:
Automotive Engineering
Boundary conditions
Classical Mechanics
Closed loops
Control
Controllers
Design
Distributed parameter systems
Dynamical Systems
Engineering
Hypotheses
Mathematical analysis
Mechanical Engineering
Original Paper
Partial differential equations
Random walk theory
Sliding mode control
Vibration
Wave equations
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Summary:We study the sliding mode control (SMC) design for unstable fractional heat and wave equations involving unknown external disturbances, respectively. In the case that the disturbance vanishes, a backstepping transform is constructed at first to stabilize the considered system in Mittag-Leffler (M-L) sense. When the disturbance flows into the boundary, sliding mode controllers are provided and the reaching conditions are also verified for fractional heat and wave systems, respectively. In the light of the Riesz basis approach, the well-posedness and closed-loop algebraic stability conclusions are established for fractional partial differential inclusion systems with discontinuous boundary conditions. As a by-product, a longtime unsolved problems raised in [ Nonlinear Dynam , 38 (2004), 339-354], which is the first contribution about the boundary feedback stabilization control for fractional partial differential equations (PDEs), are completely solved with rigorous proof.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-022-07897-3