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Keywords:
Korteweg–de Vries–Burgers equation; dynamic boundary control; uncertainty; globally exponential stabilization
Korteweg–de Vries–Burgers equation; dynamic boundary control; uncertainty; globally exponential stabilization
Summary:
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.
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