Master Degree / Yüksek Lisans Tezleri

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Access Right: Open AccessInstitution Author: search.filters.institutionAuthor.Arabacı, Eda

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  • Master Thesis
    Boundary Controller and Observer Design for Korteweg-De Vries Type Equations
    (Izmir Institute of Technology, 2017) Arabacı, Eda; Özsarı, Türker; Özsarı, Türker; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    This thesis studies the back-stepping boundary controllability of Korteweg-de Vries (KdV) type equations posed on a bounded interval. The results on the back-stepping controllability of the KdV equation obtained in Cerpa and Coron (2013) and Cerpa (2012) are reviewed and extended to the KdV-Burgers (KdVB) equation. The stability of the KdVB equation is boosted to any desired exponential rate for sufficiently small initial data with a boundary feedback controller acting on the Dirichlet boundary condition. Moreover, the case that there is no full access to the system is considered. For these kinds of systems, an observer is constructed assuming an appropriate boundary measurement is available. The ideas about designing output feedback control for the KdV equation presented in Marx and Cerpa (2016), and Hasan (2016) are reviewed and extended to the KdVB model.