Geodesic
Inverse optimal dynamic boundary control for uncertain Korteweg-de Vries-Burgers equation
Kybernetika, Tome 60 (2024) no. 6, pp. 797-818 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We investigate Korteweg-de Vries-Burgers (KdVB) equation, where the dissipation and dispersion coefficients are unknown, but their lower bounds are known. First, we establish dynamic boundary controls with update laws to globally exponentially stabilize this uncertain system. Secondly, we demonstrate that the dynamic boundary control design is suboptimal to a meaningful functional after some minor modifications of the dynamic boundary controls. In addition, we also consider dynamic boundary controls for the case of unknown dissipation or dispersion coefficients, and obtain corresponding results. Finally, three examples are used to demonstrate the effectiveness of the proposed control design.
We investigate Korteweg-de Vries-Burgers (KdVB) equation, where the dissipation and dispersion coefficients are unknown, but their lower bounds are known. First, we establish dynamic boundary controls with update laws to globally exponentially stabilize this uncertain system. Secondly, we demonstrate that the dynamic boundary control design is suboptimal to a meaningful functional after some minor modifications of the dynamic boundary controls. In addition, we also consider dynamic boundary controls for the case of unknown dissipation or dispersion coefficients, and obtain corresponding results. Finally, three examples are used to demonstrate the effectiveness of the proposed control design.
DOI : 10.14736/kyb-2024-6-0797
Classification : 93Cxx, 93Dxx
Keywords: Korteweg–de Vries–Burgers equation; dynamic boundary control; uncertainty; globally exponential stabilization 
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     author = {Cai, Xiushan and Lin, Yuhang and Lin, Cong and Liu, Leipo},
     title = {Inverse optimal dynamic boundary control for uncertain {Korteweg-de} {Vries-Burgers} equation},
     journal = {Kybernetika},
     pages = {797--818},
     year = {2024},
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     number = {6},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2024-6-0797/}
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Cai, Xiushan; Lin, Yuhang; Lin, Cong; Liu, Leipo. Inverse optimal dynamic boundary control for uncertain Korteweg-de Vries-Burgers equation. Kybernetika, Tome 60 (2024) no. 6, pp. 797-818. doi: 10.14736/kyb-2024-6-0797

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