Boundary controllability of a system modelling a partially immersed obstacle
ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 80

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) time-dependent 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.

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DOI : 10.1051/cocv/2021076
Classification : 35L50, 35L65, 93B05, 93C20
Keywords: Nonlinear shallow water equations, exact controllability, nodal profile controllability, boundary control, semi-global piecewise $$1 solution 
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     title = {Boundary controllability of a system modelling a partially immersed obstacle},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     year = {2021},
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     doi = {10.1051/cocv/2021076},
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     url = {https://www.numdam.org/articles/10.1051/cocv/2021076/}
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Vergara-Hermosilla, G.; Leugering, G.; Wang, Y. Boundary controllability of a system modelling a partially immersed obstacle. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 80. doi: 10.1051/cocv/2021076

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