Volume 27, 2021
|Number of page(s)||15|
|Published online||22 July 2021|
Boundary controllability of a system modelling a partially immersed obstacle
Institut de Mathématiques de Bordeaux, Université de Bordeaux, 351,
cours de la Liberation
2 Department of Mathematics, Friedrich-Alexander-Universität Erlangen-Nürnberg Cauerstrasse 11, 91058 Erlangen, Germany.
* Corresponding author: email@example.com
Accepted: 30 June 2021
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.
Mathematics Subject Classification: 35L50 / 35L65 / 93B05 / 93C20
Key words: Nonlinear shallow water equations / exact controllability / nodal profile controllability / boundary control / semi-global piecewise C1 solution
© The authors. Published by EDP Sciences, SMAI 2021
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