Kybernetika 60 no. 6, 797-818, 2024

Inverse optimal dynamic boundary control for uncertain Korteweg-de Vries-Burgers equation

Xiushan Cai, Yuhang Lin, Cong Lin and Leipo LiuDOI: 10.14736/kyb-2024-6-0797

Abstract:

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.

Keywords:

uncertainty, Korteweg-de Vries-Burgers equation, dynamic boundary control, globally exponential stabilization

Classification:

93Cxx, 93Dxx

paper.pdf

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