VERGARA-HERMOSILLA, Gastón; LEUGERING, Günter; WANG, Yue

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VERGARA-HERMOSILLA, Gastón
Institut de Mathématiques de Bordeaux [IMB]

LEUGERING, Günter
Friedrich-Alexander Universität Erlangen-Nürnberg = University of Erlangen-Nuremberg [FAU]

WANG, Yue
Friedrich-Alexander Universität Erlangen-Nürnberg = University of Erlangen-Nuremberg [FAU]

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In this paper, we address the problem of boundary controllability for the one-dimensional nonlinear shallow water system, describing the free surface flow of water as well as the flow under a fixed gate structure. The system of differential equations considered can be interpreted as a simplified model of a particular type of wave energy device converter called oscillating water column. The physical requirements naturally lead to the problem of exact controllability in a prescribed region. In particular, we use the concept of nodal profile controllability in which at a given point (the node) timedependent profiles for the states are required to be reachable by boundary controls. By rewriting the system into a hyperbolic system with nonlocal boundary conditions, we at first establish the semi-global classical solutions of the system, then get the local controllability and nodal profile using a constructive method. In addition, based on this constructive process, we provide an algorithmic concept to calculate the required boundary control function for generating a solution for solving these control problem.< Réduire

Mots clés en anglais

Nonlinear shallow water equations

Exact controllability

Nodal profile controllability

Boundary control

Semi-global piecewise C1 solution

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Boundary controllability of a system modelling a partially immersed obstacle

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Résumé en anglais

Mots clés en anglais

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